deal.II AUTHORS, but are included by permission. For details, consult the
stated licenses below.
-lagrange_basis
-==============
-
-A Maple script to compute the coefficients of the LagrangeEquidistant
-basis functions of degree p. Written by Ralf Hartmann.
-
-
-lapack_templates
-================
-
-A small perl script for automatically generating lapack function
-definitions. Distributed under the same license as the deal.II library.
-
mesh_conversion
===============
+## ---------------------------------------------------------------------
+## $Id$
+##
+## Copyright (C) 2001 - 2013 by the deal.II authors
+##
+## This file is part of the deal.II library.
+##
+## The deal.II library is free software; you can use it, redistribute
+## it, and/or modify it under the terms of the GNU Lesser General
+## Public License as published by the Free Software Foundation; either
+## version 2.1 of the License, or (at your option) any later version.
+## The full text of the license can be found in the file LICENSE at
+## the top level of the deal.II distribution.
+##
+## ---------------------------------------------------------------------
+
+#
+# Author: Ralf Hartmann, 2001
+#
+
+#
# Maple script to compute the coefficients of the LagrangeEquidistant
# basis functions of degree p. These are used as shape functions for
# Qp elements. For higher p just change variable p in line 10.
-# Call
+# Call
# perl -p -e 's/ *t0 = (.*);\n/ $1/g;' lagrange_txt
# to get a c-code ready to be copied into the source codes.
-# $Id$
-# Ralf Hartmann, 2001
+#
p := 10:
n_functions := p+1:
-
+
# first compute the support points
support_points := array(0..n_functions-1):
for i from 0 to n_functions-1 do
- support_points[i] := i/(n_functions-1):
- od;
+ support_points[i] := i/(n_functions-1):
+ od;
poly := array(0..n_functions-1):
for i from 0 to n_functions-1 do
# note that the interp function wants vectors indexed from
- # one and not from zero.
+ # one and not from zero.
values := array(1..n_functions):
for j from 1 to n_functions do
values[j] := 0:
- od:
+ od:
values[i+1] := 1:
shifted_support_points := array (1..n_functions):
for j from 1 to n_functions do
shifted_support_points[j] := support_points[j-1]:
od:
-
+
poly[i] := interp (shifted_support_points, values, x):
od:
-
+
readlib(C):
writeto(lagrange_output):
printf(` case %d:\n {\n static const double x%d[%d]=\n {`, p,p,(p+1)*(p+1)):
od:
C(b[0]):
for j from 1 to n_functions-1 do
- printf(`,`):
+ printf(`,`):
C(b[j]):
od:
if (i<n_functions-1) then
#! /bin/bash
-
#
-# Copyright 2010 - 2013 Carsten Burstedde
+# This file is part of p4est [1].
+# p4est is a C library to manage a collection (a forest) of multiple
+# connected adaptive quadtrees or octrees in parallel.
+#
+# Copyright (C) 2010 The University of Texas System
+# Written by Carsten Burstedde, Lucas C. Wilcox, and Tobin Isaac
# Modified 2010 by Wolfgang Bangerth
# Modified 2010 by Timo Heister
+# Modified 2013 by Matthias Maier
+#
+# p4est is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# [1] http://www.p4est.org
#
# This program comes with ABSOLUTELY NO WARRANTY.
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2007 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
* @page changes_between_6_0_and_6_1 Changes between Version 6.0 and 6.1
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2009 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
* @page changes_between_6_1_and_6_2 Changes between Version 6.1 and 6.2
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2009 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
* @page changes_between_6_2_0_and_6_2_1 Changes between Version 6.2.0 and 6.2.1
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2010 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
* @page changes_between_6_2_and_6_3 Changes between Version 6.2 and 6.3
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2010 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
* @page changes_between_6_3_0_and_6_3_1 Changes between Version 6.3.0 and 6.3.1
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2011 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
* @page changes_between_6_3_and_7_0 Changes between Version 6.3 and 7.0
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2011 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
* @page changes_between_7_0_and_7_1 Changes between Version 7.0 and 7.1
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2012 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
* @page changes_between_7_1_and_7_2 Changes between Version 7.1 and 7.2
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
* @page changes_between_7_2_and_7_3 Changes between Version 7.2 and 7.3
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
* @page changes_between_7_3_and_8_0 Changes between Version 7.3 and 8.0
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
/**
// * @page changes_after_8_0 Changes after Version 8.0
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@MastersThesis{Ban98,
- author = {Wolfgang Bangerth},
- title = {{A}daptive {F}inite-{E}lemente-{M}ethoden zur {L}{\"o}sung der
- {W}ellengleichung mit {A}nwendung in der {P}hysik der {S}onne},
- school = {Institut f{\"u}r Angewandte Mathematik, Universit{\"a}t Heidelberg},
- year = 1998,
- type = {Diplomarbeit}
-}
-
-
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<H3>Abstract:</H3>
-<DIR>
- In this work, adaptive concepts for the numerical solution of the wave
- equation in inhomogeneous media are derived and applied to an example
- taken from the physics of the solar atmosphere. The main focus is on ways
- to estimate the error in the numerical solution with regard to arbitrary
- functionals, i.e. quantities of interest, and the use of these estimates
- for the generation of computational meshes best suited for the evaluation
- of this functional.
-
-<p>
-
- Advantages and difficulties of this method are presented. In particular,
- it is shown that the proposed approach is significantly better in many
- cases than previous adaptive schemes not taking into account the quantity
- of interest. Cases involving nonlinear functionals and in which the
- approach fails, are presented along with theoretical explanations and
- numerical evidence of the reasons for this.
-
-<p>
-
- The proposed methods are applied to a simple model from the physics of the
- solar atmosphere and the propagation of linear acoustic waves is computed.
- The fraction of the wave energy that passes the chromosphere-corona
- transition is computed to good accuracy.
-</DIR>
-
-<P>
-<BR><HR>
-<ADDRESS>
-<I>Wolfgang Bangerth</I>
-<BR><I>1999-09-10</I>
-</ADDRESS>
-</BODY>
-</HTML>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@TechReport{BK99tr,
- author = {Wolfgang Bangerth and Guido Kanschat},
- title = {Concepts for Object-Oriented Finite Element Software -- the
- \texttt{deal.II} library},
- institution = {IWR Heidelberg},
- year = 1999,
- type = {{P}reprint 99-43 ({SFB} 359)},
- month = oct
-}
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<H3>Abstract:</H3>
-<DIR>
-
-An overview of the <TT>deal.II</TT> library is given. This library provides
- the functionality needed by modern numerical software used in the finite
- element solution of partial differential equations, offering adaptively
- refined meshes, different finite element classes, multigrid solvers and
- support for one, two and three spatial dimensions.
-
-<P>
-
- We give a description of the basic design criteria used in the
- development of the library and how they were transformed into actual
- code, and some examples of the use of the library in numerical
- analysis.
-
-</DIR>
-<P>
-<BR><HR>
-<ADDRESS>
-<I>Wolfgang Bangerth</I>
-<BR><I>1999-09-10</I>
-</ADDRESS>
-</BODY>
-</HTML>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-
-@Article{BR01a,
- author = {Wolfgang Bangerth and Rolf Rannacher},
- title = {Adaptive Finite Element Techniques for the Acoustic Wave Equation},
- journal = {J. Comput. Acoustics},
- year = 2001,
- volume = 9,
- number = 2,
- pages = {575--591}
-}
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<H3>Abstract:</H3>
-<DIR>
- We present an adaptive finite element method for solving the acoustic
- wave equation. Using a global duality argument and Galerkin orthogonality,
- we derive an identity for the error with respect to an arbitrary functional
- output of the solution. The error identity is evaluated by solving the
- dual problem numerically. The resulting local cell-wise error indicators
- are used in adaptation process. In this way, the space-time mesh can be
- tailored for the efficient computation of the quantity of interest.
- We give an overview of the implementation of the proposed method and
- illustrate its performance by several numerical examples.
-</DIR>
-<P>
-<BR><HR>
-<ADDRESS>
-<I>Wolfgang Bangerth</I>
-<BR><I>1999-09-10</I>
-</ADDRESS>
-</BODY>
-</HTML>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-
-@Article{BR99b,
- author = {Wolfgang Bangerth and Rolf Rannacher},
- title = {Finite element approximation of the acoustic wave equation:
- {E}rror control and mesh adaptation},
- journal = {East--West J. Numer. Math.},
- year = 1999,
- volume = 7,
- number = 4,
- pages = {263--282}
-}
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<H3>Abstract:</H3>
-<DIR>
-We present an approach to solving the acoustic wave equation by adaptive
- finite element methods. Using a global duality argument and Galerkin
- orthogonality, we obtain a residual-based error representation with respect to
- an
- arbitrary functional of the solution. This results in numerically
- evaluatable error estimates which are used for mesh refinement. In this way,
- very economical and highly localized space-time
- meshes can be generated which are tailored to the efficient computation of
- the quantity of interest. We demonstrate the performance and some of the
- mechanisms acting in our approach by numerical examples.
-</DIR>
-<P>
-<BR><HR>
-<ADDRESS>
-<I>Wolfgang Bangerth</I>
-<BR><I>1999-09-10</I>
-</ADDRESS>
-</BODY>
-</HTML>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@InProceedings{Ban00w,
- author = {Wolfgang Bangerth},
- title = {Mesh Adaptivity and Error Control for a Finite Element
- Approximation of the Elastic Wave
- Equation},
- booktitle = {Proceedings of the Fifth International Conference on Mathematical
- and Numerical Aspects of Wave Propagation (Waves2000), Santiago
- de Compostela, Spain, 2000},
- pages = {725--729},
- year = 2000,
- editor = {Alfredo Berm\'udez and Dolores G\'omez and Christophe Hazard and
- Patrick Joly and Jean E. Roberts},
- publisher = {SIAM}
-}
-
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<H3>Abstract:</H3>
-<DIR>
- An approach to solve the elastic wave equation by adaptive finite elements
- is presented. The strategy for adaptivity is founded on an a posteriori
- residual-based error estimate, where the error is measured with respect to
- an arbitrary target functional, allowing to focus the simulation to the
- computation of a given quantity of interest. The cell-wise error indicators
- are computationally evaluated and used for refinement of the space-time
- mesh. The resulting grids are usually highly localized and tailored to the
- target functional. The performance of the approach is demonstrated with two
- examples.
-
-</DIR>
-<P>
-<BR><HR>
-<ADDRESS>
-<I>Wolfgang Bangerth</I>
-<BR><I>1999-09-10</I>
-</ADDRESS>
-</BODY>
-</HTML>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-
-@TechReport{Ban00mt,
- author = {Wolfgang Bangerth},
- title = {Multi-threading support in \texttt{deal.II}},
- institution = SFB,
- year = 2000,
- type = {{P}reprint},
- number = {2000-11},
- month = apr
-}
-
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<H3>Abstract:</H3>
-<DIR>
- In this report, we describe the implementational techniques of
- multi-threading support in deal.II, which we use for the
- parallelization of independent operations. Writing threaded programs in
- C++ is obstructed by two problems: operating system dependent
- interfaces and that these interfaces are created for C programs
- rather than for C++. We present our solutions to these problems and
- describe first experiences using multi-threading in deal.II.
-</DIR>
-<P>
-<BR><HR>
-<ADDRESS>
-<I>Wolfgang Bangerth</I>
-<BR><I>2000-03-31</I>
-</ADDRESS>
-</BODY>
-</HTML>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-
-@InProceedings{Ban00i,
- author = {Wolfgang Bangerth},
- title = {Using Modern Features of {C}++ for Adaptive Finite Element Methods:
- {D}imension-Independent Programming in deal.{I}{I}},
- booktitle = {Proceedings of the 16th IMACS World Congress 2000, Lausanne,
- Switzerland, 2000},
- year = 2000,
- editor = {Michel Deville and Robert Owens},
- note = {{D}ocument Sessions/118-1}
-}
-
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<H3>Abstract:</H3>
-<DIR>
- <p>
- Modern finite element software tends to become increasingly complex.
- Techniques like adaptive meshes, error estimation, multigrid methods, or
- <em>hp</em> finite elements require the programmer to work with extremely
- complicated data structures and sophisticated algorithms. Designing programs
- in a maintainable and expandable way while retaining run time efficiency has
- therefore become a major task in applied numerical analysis. In our
- experience, this task can only be fulfilled by using modern programming
- languages and tools.
- </p>
-
- <p>
- We will show how modern aspects of the C++ programming language, in
- particular templates, can be used to write algorithms for finite element
- programs in a dimension-independent way. This enables us to test algorithms
- in one or two space dimensions while using the same program for large scale
- computations in three space dimensions as well. It will be demonstrated that
- this is even possible without much loss in efficiency since tests for the
- actual space dimension at run time can almost completely be avoided.
- </p>
-
- <p>
- The idiom above is one of several modern aspects of C++ used in the design
- of the finite element library deal.II developed at the University
- of Heidelberg. We will give a sketch of its implementation and examples how
- it is used.
- </p>
-</DIR>
-<P>
-<BR><HR>
-<ADDRESS>
-<I>Wolfgang Bangerth</I>
-<BR><I>2000-03-31</I>
-</ADDRESS>
-</BODY>
-</HTML>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@TechReport{CKPS00,
- author = {Cockburn, Bernardo and Kanschat, Guido and Perugia, Ilaria and
- Schötzau, Dominik},
- title = {Superconvergence of the Local Discontinuous Galerkin
- Method for Elliptic Problems on Cartesian Grids},
- institution = UMSI,
- year = 2000,
- number = {2000/71}
-}
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-<h1>Superconvergence of the Local Discontinuous Galerkin
- Method for Elliptic Problems on Cartesian Grids</h1>
-Bernardo Cockburn, <a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
- target="_top">Guido Kanschat</a>, Ilaria Perugia, Dominik Schötzau
-<h3>Abstract</h3>
-
-<dir>
- In this paper, we present a super-convergence result for the Local
-Discontinuous Galerkin method for a model elliptic problem on
-Cartesian grids. We identify a <em>special</em> numerical flux for
-which the <em>L<sup>2</sup></em>-norm of the gradient and the
-<em>L<sup>2</sup></em>-norm of the potential are of order
-<em>k+1/2</em> and <em>k+1</em>, respectively, when tensor product
-polynomials of degree at most <em>k</em> are used; for arbitrary
-meshes, this special LDG method gives only the orders of convergence
-of <em>k</em> and <em>k+1/2</em>, respectively. We present a series
-of numerical examples which establish the sharpness of our theoretical
-results.
-</dir>
-
-</body>
-</html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@TechReport{CKSS00,
- author = {Cockburn, Bernardo and Kanschat, Guido and Sch{\"o}tzau, Dominik and Schwab, Christoph},
- title = {Local discontinuous {G}alerkin methods for the {S}tokes
- system},
- institution = IMA,
- year = 2000,
- number = 1728,
- month = {oct},
- note = {submitted to SIAM J. Numer. Anal.}
-}
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-<h1>Local discontinuous Galerkin methods for the Stokes system</h1>
-Bernardo Cockburn,
- <a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
- target="_top">Guido Kanschat</a>, Dominik Schötzau, Christoph Schwab
-<h3>Abstract</h3>
-
-<dir>
-In this paper, we introduce and analyze local discontinuous Galerkin
-methods for the Stokes system. For arbitrary meshes with hanging
-nodes and elements of various shapes we derive a priori estimates for
-the <i>L<sup>2</sup></i>-norm of the errors in the velocities and
-the pressure. We show that <b>optimal</b> order estimates are
-obtained when polynomials of degree <i>k</i> are used for each
-component of the velocity and polynomials of degree <i>k</i>-1 for the
-pressure, for any <i>k</i>>1. We also consider the case in which
-<b>all</b> the unknowns are approximated with polynomials of degree <i>k</i>
-and show that, although the orders of convergence remain the same, the
-method is more efficient. Numerical experiments verifying these facts
-are displayed.
-</dir>
-
-</body>
-</html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@Article{GK03,
- title = {A Multilevel Discontinuous {G}alerkin Method},
- author = {Gopalakrishnan, J. and Kanschat, G.},
- journal = {Numer. Math.},
- number = {3},
- pages = {527--550},
- volume = {95},
- year = {2003}
-}
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-<h1>A Multilevel Discontinuous Galerkin Method</h1>
-J. Gopalakrishnan,
- <a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
- target="_top">G. Kanschat</a>
-<h3>Abstract</h3>
-
-<dir>
-A variable V-cycle preconditioner for an interior penalty finite
-element discretization for elliptic problems is presented. An analysis
-under a mild regularity assumption shows that the preconditioner is
-uniform. The interior penalty method is then combined with a
-discontinuous Galerkin scheme to arrive at a discretization scheme for
-an advection-diffusion problem, for which an error estimate is
-proved. A multigrid algorithm for this method
-is presented, and numerical experiments indicating its robustness
-with respect to diffusion coefficient are reported.
-</dir>
-
-</body>
-</html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@InProceedings{Har00a,
- author = {Ralf Hartmann},
- title = {Adaptive {FE} {M}ethods for {C}onservation {E}quations},
- booktitle = {Hyperbolic Problems: theory, numerics, applications: eighth international confere
-nce in {M}agdeburg, February, March 2000},
- year = 2001,
- editor = {Heinrich Freist{\"u}hler and Gerald Warnecke},
- volume = 2,
- series = {International series of numerical mathematics; Vol. 141},
- publisher = {Birkh{\"a}user, Basel},
- pages = {495--503}
-}
-
-
-
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<H3>Abstract:</H3>
-<DIR>
-
- We present an approach to solving conservation equations by the
- adaptive discontinuous Galerkin finite element method
- (DG-method). Using a global duality argument and Galerkin
- orthogonality, we obtain a residual-based error representation for the
- error with respect to an arbitrary functional of the solution. This
- results in local indicators that can be evaluated numerically and
- which are used for adaptive mesh refinement and coarsening. In this
- way, very economical and highly localized meshes can be generated
- which are tailored to the cost-efficient computation of the quantity
- of interest. We demonstrate the main ingredients of this approach of a
- posteriori error estimation, test the quality of the error estimator
- and the efficiency of the meshes by some numerical examples.
-
-</DIR>
-<P>
-<BR><HR>
-<ADDRESS>
-<I>Ralf Hartmann</I>
-<BR><I>2000-03-31</I>
-</ADDRESS>
-</BODY>
-</HTML>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<H3>Abstract:</H3>
-<DIR>
-In this thesis, the <em>dual weighted residual</em> a posteriori error
-estimator is studied for error estimation in arbitrary (linear)
-functionals. The main focus is the construction of optimal meshes for
-the solution of elliptic differential equations.
-The quality of the meshes is measured by the effort to gain a suitable
-solution of the differential equation and by the effort to generate
-the mesh.
-The <em>dual weighted error estimator</em> is used for <em>hierarchical
-mesh refinemant</em>. One chapter discusses the application of the
-error estimator for optimal anisotropic meshes.
-
-</DIR>
-<P>
-<BR><HR>
-<ADDRESS>
-<I>Thomas Richter</I>
-<BR><I>2001-01-01</I>
-</ADDRESS>
-</BODY>
-</HTML>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@PhdThesis{Ban02,
- author = {Wolfgang Bangerth},
- title = {Adaptive Finite Element Methods for the Identification
- of Distributed Coefficient in Partial Differential
- Equations},
- school = {University of Heidelberg},
- year = 2002
-}
-
-
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<H3>Abstract:</H3>
-<DIR>
- <p>
- In this thesis, we develop adaptive finite element methods for
- parameter estimation problems involving partial differential
- equations as constraints. In these so-called <em>Inverse
- Problems</em>, the goal is the identification of a distributed
- coefficient in a PDE by measurements of the state variable. This has
- important applications where material parameters are to be
- recovered, but only indirect measurements are possible, such as
- identification of the underground structure from seismic
- measurements, or in nondestructive material testing.
- </p>
-
- <p>
- For this kind of problems, we develop adaptive finite element
- discretizations based on error estimates, where the estimates are
- both for the error in the minimization functional (i.e. of
- ``energy-type'') as well as in arbitrary functionals. Furthermore,
- methods are developed to handle constraints on the sought
- coefficients, based on active set strategies. The methods developed
- are numerically tested at a number of large scale inverse problems
- realizing some types of inverse problems that actually occur in
- applications.
- </p>
-</DIR>
-<P>
-<BR><HR>
-<ADDRESS>
-<I>Wolfgang Bangerth</I>
-<BR><I>2002-04-16</I>
-</ADDRESS>
-</BODY>
-</HTML>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-<h1>LDG methods for Stokes flow problems</h1>
-Bernardo Cockburn,
- <a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
- target="_top">Guido Kanschat</a>, Dominik Schötzau
-<h3>Abstract</h3>
-
-<dir>
-We review the development of local discontinuous
-Galerkin methods for
-the Stokes problem in incompressible fluid flow.
-We explain the derivation of these methods
-and present the corresponding error estimates.
-The case of natural boundary conditions is treated.
-A series of numerical examples are shown.
-</dir>
-
-</body>
-</html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-<h1>The local discontinuous Galerkin method for the Oseen equations</h1>
-Bernardo Cockburn,
- <a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
- target="_top">Guido Kanschat</a>, Dominik Schötzau
-<h3>Abstract</h3>
-
-<dir>
-We introduce and analyze the local discontinuous Galerkin method for the
-Oseen equations of incompressible fluid flow. For a class of shape-regular
-meshes with hanging nodes, we derive optimal
-a priori estimates for the errors
-in the velocity and the pressure in L<sup>2</sup>- and negative-order norms.
-Numerical experiments are presented which verify these theoretical results
-and show that the method performs well for a wide range of Reynolds numbers.
-\</dir>
-
-</body>
-</html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@PhdThesis{Har02,
- author = {Ralf Hartmann},
- title = {Adaptive Finite Element Methods for the
- Compressible Euler Equations},
- school = {University of Heidelberg},
- year = 2002
-}
-
-
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<h3>Abstract:</h3>
-<dir>
-In this thesis we introduce a discontinuous Galerkin method for the
-numerical solution of hyperbolic conversation laws, as for example the
-compressible Euler equations of gas dynamics. Based on this finite
-element method, we develop an adaptive algorithm for the efficient
-computation of physically relevant quantities of the solution. This
-includes <em>a posteriori</em> error estimation of the error in the
-computed quantity as well as adaptive mesh design specifically
-tailored to the efficient computation of this quantity. We illustrate
-this approach by several different hyperbolic problems in combination
-with various different target quantities, including the efficient
-computation of drag and lift coefficients of airfoils immersed in
-inviscid compressible gas flows.
-<br>
-<br>
-In particular, this work includes following issues
-<ul>
- <li> <p>
- Discretisation:
- <ul>
- <li> Streamline diffusion and discontinuous Galerkin method
- for a scalar hyperbolic problem: <br> comparison with respect to
- accuracy and conservation properties
- <li> Discontinuous Galerkin method for the compressible Euler equations
- <li> Use of shock-capturing
- <li> Higher order boundary approximation at reflective boundaries
- <li> Solution of the nonlinear and the linear problems
- <li> Mesh generation for airfoil computations
- </ul>
- </p>
-
- <li> <p>
- A posteriori error estimation and adaptivity:
- <ul>
- <li> Derivation (by duality argument) of error estimates with
- respect to arbitrary target functionals
-
- <li> Question of well-posedness of the dual problem
-
- <li> Approximation of the error representation by numerical
- approximation of the dual solution
-
- <li> Adaptive algorithm tailored to the efficient computation
- of the quantity of interest
- </ul>
- </p>
-
- <li> <p> Numerical Examples illustrating the performance of the
- error estimation and the adaptive grid refinement for a wide range
- of hyperbolic problems including
- <ul>
- <li> the linear advection equation
- <li> the 1D inviscid Burgers equation
- <li> the Buckley-Leverett equation
- <li> the 1D compressible Euler equations
- <li> and several examples for the 2D compressible Euler equations.
- </ul>
- and for a variety of target functionals (quantities) including
- <ul>
- <li> drag and lift coefficients of airfoils
- <li> pressure point values
- <li> weighted boundary integrals
- </ul>
- </p>
-
- <li> <p>
- Appendices
- <ul>
- <li> Full description of exact solutions to hyperbolic
- problems treated in numerical examples
-
- <li> Implementational details of finite elements with curved
- boundaries
-
- </ul>
-</dir>
-</body>
-</html>
-
-
-
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@Article{HH02a,
- author = {Ralf Hartmann and Paul Houston},
- title = {Adaptive Discontinuous {G}alerkin Finite Element Methods
- for Nonlinear Hyperbolic Conservation Laws},
- journal = {SIAM J. Sci. Comp.},
- year = {2002},
- volume = 24,
- pages = {979--1004}
-}
-
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-
-<h1>Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws</h1>
-<a href="http://ganymed.iwr.uni-heidelberg.de/~hartmann"
- target="_top">R. Hartmann</a> and P. Houston
-
-
-<h3>Abstract:</h3>
-<dir>
-We consider the <em>a posteriori</em> error analysis
-and adaptive mesh design for discontinuous Galerkin finite
-element approximations to systems of nonlinear
-hyperbolic conservation laws.
-In particular, we discuss the question of error estimation for general
-linear and nonlinear functionals of the solution; typical examples
-include the
-outflow flux, local average and pointwise value, as well as the lift
-and drag coefficients of a body immersed in an inviscid fluid.
-By employing a duality argument, we derive so-called weighted or Type I
-<em>a posteriori</em> error bounds; in these error estimates
-the element--residuals are multiplied by local weights involving
-the solution of a certain dual problem. Based on these <em>a posteriori</em>
-bounds, we design and implement the corresponding adaptive algorithm
-to ensure efficient and reliable control of the error in the
-computed functional. The theoretical results are illustrated by a series of
-numerical experiments. In particular, we demonstrate the superiority
-of the proposed approach over standard mesh refinement algorithms which employ
-<em>ad hoc</em> error indicators.
-</dir>
-
-</body>
-</html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-
-@Article{HH02b,
- author = {Ralf Hartmann and Paul Houston},
- title = {Adaptive Discontinuous {G}alerkin Finite Element Methods
- for the Compressible {E}uler Equations},
- journal = {J. Comp. Phys.},
- year = 2002,
- volume = 183,
- number = 2,
- pages = {508--531}
-}
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-<h1>Adaptive Discontinuous Galerkin Finite Element Methods for the Compressible Euler Equations</h1>
-<a href="http://ganymed.iwr.uni-heidelberg.de/~hartmann"
- target="_top">R. Hartmann</a> and P. Houston
-
-<h3>Abstract:</h3>
-<dir>
-In this paper a recently developed approach
- for the design of
- adaptive discontinuous Galerkin finite element approximations
- is applied to physically relevant problems arising in inviscid compressible
- fluid flows governed by the
- Euler equations of gas dynamics. In particular, we employ so--called
- weighted or Type I <em>a posteriori</em> error bounds to drive adaptive
- finite element algorithms for the estimation of
- the error measured in terms of general linear and nonlinear target
- functionals of the solution; typical examples considered here include
- the point evaluation of a component of the solution vector, and the
- drag and lift coefficients of a body immersed in an inviscid fluid.
- This general approach leads to the design of
- economical finite element meshes specifically tailored to the computation
- of the target functional of interest, as well as providing reliable and
- efficient error estimation. Indeed, the superiority of the proposed
- approach over standard mesh refinement algorithms which employ <em>
- ad hoc</em> error indicators will be illustrated by a series of
- numerical experiments; here, we consider
- transonic flow through a nozzle, as well as subsonic, transonic and
- supersonic flows around different airfoil geometries.
-
-</dir>
-</body>
-</html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-<h1>Multi-level Preconditioners for the interior penalty method</h1>
-<a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
- target="_top">Guido Kanschat</a>
-<h3>Abstract</h3>
-
-<dir>
- The analysis of the variable V-cycle for interior penalty
- discretization of Poisson's equation is reviewed. The performance of
- the analyzed method is compared to several variants. Numerical
- results for the LDG method are presented.
-\</dir>
-
-</body>
-</html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@InProceedings{HH03a,
- author = {Paul Houston and Ralf Hartmann},
- title = {Goal--Oriented A Posteriori Error Estimation for Compressible Fluid Flows},
- booktitle = {Numerical Mathematics and Advanced Applications},
- pages = {775--784},
- year = 2003,
- editor = {F. Brezzi and A. Buffa and S. Corsaro and A. Murli},
- publisher = {Springer}
-}
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-<h1>Goal-Oriented A Posteriori Error Estimation for Compressible Fluid Flows</h1>
-<a href="http://ganymed.iwr.uni-heidelberg.de/~hartmann"
- target="_top">R. Hartmann</a> and P. Houston
-
-
-<h3>Abstract:</h3>
-<dir>
- <p>
- We consider so-called `goal-oriented' <em>a posteriori</em> error
- estimation for discontinuous Galerkin finite element approximations to
- the compressible Euler equations of gas dynamics. By employing a
- hyperbolic duality argument, we derive weighted, or Type I, <em>a
- posteriori</em> error estimates which bound the error measured in
- terms of certain target functionals of real or physical interest. The
- practical advantages of this general approach are illustrated by a
- series of numerical experiments.
- </p>
-</dir>
-</body>
-</html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
- <body>
- <pre>
-
-@InProceedings{HH03b,
- author = {Ralf Hartmann and Paul Houston},
- title = {Goal-Oriented A Posteriori Error Estimation for Multiple Target Functionals},
- booktitle = {Hyperbolic problems: theory, numerics, applications},
- pages = {579-588},
- year = 2003,
- editor = {Thomas Y. Hou and Eitan Tadmor},
- publisher = {Springer},
-}
-
-</pre></body></html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <body>
-
-<h1> Goal-Oriented A Posteriori Error Estimation for Multiple Target Functionals</h1>
-<a href="http://ganymed.iwr.uni-heidelberg.de/~hartmann"
- target="_top">R. Hartmann</a> and P. Houston
-
-
-<h3>Abstract:</h3>
-<dir>
- <p>
- In many applications the quantities of interest are a series of
- target functionals of the solution to the governing system of
- partial differential equations rather than the solution itself. For
- example, in the field of aerodynamics, examples include the drag and
- lift coefficients of an airfoil immersed into a fluid, the pressure
- difference between the leading and trailing edges of the airfoil and
- point evaluations of the density or pressure on the profile of the
- airfoil. While traditionally these quantities are measured in wind
- tunnel experiments, nowadays these experiments are increasingly
- replaced by numerical simulations aiming to predict these quantities
- to a high level of accuracy.
- <br>
- In a series of previous articles, we have developed the theory of
- goal--oriented <em>a posteriori</em> error estimation for
- discontinuous Galerkin methods applied to inviscid compressible
- fluid flows. On the basis of Type I <em>a posteriori</em> bounds we
- considered the design of adaptive finite element algorithms that are
- capable of generating optimal meshes specifically tailored to the
- efficient computation of a <em>single</em> target functional of
- practical interest. The purpose of the current article is to extend
- this earlier work to the case when <em>several</em> target
- functionals of the solution need to be simultaneously approximated
- to a given level of accuracy.
- </p>
-</dir>
-</body>
-</html>
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
- "http://www.w3.org/TR/REC-html40/strict.dtd">
-<html>
- <head>
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- <pre>
-
-@InCollection{HH04a,
- author = {Ralf Hartmann and Paul Houston},
- title = {Adaptive Discontinuous {G}alerkin Finite Element Methods with Interior Penalty
- for the Compressible {N}avier-{S}tokes Equations},
- booktitle = {Numerical Mathemathics and Advanced Applications, ENUMATH 2003},
- editor = {M. Feistauer and V. Doleji and P. Knobloch and K. Najzar},
- pages = {410--419},
- publisher = {Springer},
- year = 2004
-}
-
-</pre></body></html>
<br>
in Brezzi, Buffa, Corsaro, Murli: Numerical Mathematics and Advanced Applications:
ENUMATH 2001, Springer Italia, 2003
- <br>
- (<a href="2002/cks-1.html" target="body">Abstract</a>
- )
</li>
<li>
<strong>The Local Discontinuous Galerkin Method for the Oseen Equations</strong>
<br>
Math. Comput., vol. 73, pp. 569-593, 2003
- <br>
- (<a href="2002/cks-2.html" target="body">Abstract</a>)
</li>
<li>
</strong>
<br>
Numer. Math., vol. 95, pp. 527-550, 2003
- <br>
- (<a href="2000/gk.html" target="body">Abstract</a>,
- <a href="2000/gk.bib" target="body">BibTeX
- entry</a>,
- <a href="http://www.ima.umn.edu/preprints/dec2000/1735.ps">Postscript</a>)
</li>
<li>
<br>
in Brezzi, Buffa, Corsaro, Murli: Numerical Mathematics and Advanced Applications:
ENUMATH 2001, Springer Italia, 2003
- <br>
- (<a href="2002/kanschat-1.html" target="body">Abstract</a>)
</li>
<li> <a href="http://ganymed.iwr.uni-heidelberg.de/~hartmann/"
<br>
in T. Y. Hou and E. Tadmor, editors, Hyperbolic Problems:
Theory, Numerics, Applications, pp. 579-588, Springer, 2003
- <br>
- (<a href="2003/hh03b.html" target="body">Abstract</a>,
- <a href="2003/hh03b.bib" target="body">BibTeX
- entry</a>)
</li>
<li> <a href="http://ganymed.iwr.uni-heidelberg.de/~hartmann/"
<br>
In F. Brezzi, A. Buffa, S. Corsaro and A. Murli, editors,
Numerical Mathematics and Advanced Applications, pp. 775-784, Springer, 2003
- <br>
- (<a href="2003/hh03a.html" target="body">Abstract</a>,
- <a href="2003/hh03a.bib" target="body">BibTeX
- entry</a>)
</li>
<li>
</strong>
<br>
Ph.D. thesis, University of Heidelberg, 2002
- <br>
- (<a href="2002/bangerth-1.html" target="body">Abstract</a>,
- <a href="2002/bangerth-1.bib" target="body">BibTeX
- entry</a>)
</li>
<li> S. Benkler
in Mang, Rammerstorfer, Eberhardsteiner: Proceedings of the
Fifth World Congress on Computational Mechanics (WCCM V),
Vienna University of Technology, 2002
- <br>
- (<a href="2000/ckss.html" target="body">Abstract</a>,
- <a href="2000/ckss.bib" target="body">BibTeX
- entry</a>,
- <a href="http://www.ima.umn.edu/preprints/oct2000/1728.ps">Postscript</a>)
</li>
<li>
</strong>
<br>
SIAM J. Numer. Anal., vol. 40, pp. 319-343, 2002
- <br>
- (<a href="2000/ckss.html" target="body">Abstract</a>,
- <a href="2000/ckss.bib" target="body">BibTeX
- entry</a>,
- <a href="http://www.ima.umn.edu/preprints/oct2000/1728.ps">Postscript</a>)
</li>
<li>
</strong>
<br>
Ph.D. thesis, University of Heidelberg, 2002
- <br>
- (<a href="2002/har02.html" target="body">Abstract</a>,
- <a href="2002/har02.bib" target="body">BibTeX entry</a>)
</li>
<li>
</strong>
<br>
J. Comput. Phys., vol. 183, pp. 508-532, 2002.
- <br>
- (<a href="2002/hh02b.html" target="body">Abstract</a>,
- <a href="2002/hh02b.bib" target="body">BibTeX
- entry</a>)
</li>
<li>
</strong>
<br>
SIAM J. Sci. Comput., vol. 24, pp. 979-1004, 2002.
- <br>
- (<a href="2002/hh02a.html" target="body">Abstract</a>,
- <a href="2002/hh02a.bib" target="body">BibTeX
- entry</a>)
</li>
<li>
</strong>
<br>
J. Numer. Math., vol. 10, pp. 249-274, 2002
- <br>
- (<a href="2000/ckss.html" target="body">Abstract</a>,
- <a href="2000/ckss.bib" target="body">BibTeX
- entry</a>,
- <a href="http://www.ima.umn.edu/preprints/oct2000/1728.ps">Postscript</a>)
</li>
<li> F. Mohamed, M. Troyer, G. Blatter
</strong>
<br>
SIAM J. Numer. Anal. 39 (1), pp. 264-285, 2001
- <br>
- (<a href="2000/ckps.html" target="body">Abstract</a>,
- <a href="2000/ckps.bib" target="body">BibTeX
- entry</a>,
- <a href="http://www.ima.umn.edu/preprints/apr2000/1695.ps">Postscript</a>)
</li>
<li>
Approximation elliptischer Differentialgleichungen
</strong>
<br>
- Diploma thesis, University of Heidelberg, 2001 (in German) <br>
- (<a href="2001/richter-1.html" target="body">Abstract</a>)
+ Diploma thesis, University of Heidelberg, 2001 (in German)
</li>
</ol>
<br>
Proceedings of the Waves2000 conference,
held in Santiago de Compostela, Spain, July 10-14, 2000
- <br>
- (<a href="2000/bangerth-1.html" target="body">Abstract</a>,
- <a href="2000/bangerth-1.bib" target="body">BibTeX
- entry</a>)
</li>
<li>
</strong>
<br>
Preprint 2000-11 (SFB 359), IWR Heidelberg, October 1999.
- <br>
- (<a href="2000/bangerth-2.html" target="body">Abstract</a>,
- <a href="2000/bangerth-2.bib" target="body">BiBTeX entry</a>)
</li>
<li>
<br>
Proceedings of the 16th IMACS World
Congress, Lausanne, Switzerland, 2000
- <br>
- This paper is also available
- <a href="../reports/dimension-independent/index.html" target="body">online</a>.
- <br>
- (<a href="2000/bangerth-3.html" target="body">Abstract</a>,
- <a href="2000/bangerth-3.bib" target="body">BibTeX entry</a>)
</li>
<li> <a href="http://ganymed.iwr.uni-heidelberg.de/~hartmann"
<br>
International series of numerical mathematics 141: 495-503.
Birkhäuser, Basel 2001.
- <br>
- (<a href="2000/hartmann-1.html" target="body">Abstract</a>,
- <a href="2000/hartmann-1.bib" target="body">BibTeX
- entry</a>)
</li>
<li> F. Mohamed
</strong>
<br>
Preprint 99-43 (SFB 359), IWR Heidelberg, October 1999.
- <br>
- (<a href="1999/bangerth-kanschat.html" target="body">Abstract</a>,
- <a href="1999/bangerth-kanschat.bib" target="body">BibTeX
- entry</a>)
</li>
<li>
<br>
East-West Journal of Numerical Mathematics, vol. 7, no. 4 (1999),
pp. 263-282
- <br>
- (<a href="1999/bangerth-rannacher-2.html" target="body">Abstract</a>,
- <a href="1999/bangerth-rannacher-2.bib" target="body">BibTeX
- entry</a>)
</li>
<li>
<a href="http://www.math.tamu.edu/~bangerth"
<br>
Journal of Computational Acoustics, vol. 9, no. 2
(2001), pp. 575-591
- <br>
- (<a href="1999/bangerth-rannacher-1.html" target="body">Abstract</a>,
- <a href="1999/bangerth-rannacher-1.bib" target="body">BibTeX
- entry</a>)
</li>
<li>
</strong>
<br>
Diploma thesis, University of Heidelberg, 1998 (in German)
- <br>
- (<a href="1998/bangerth.html" target="body">Abstract</a>,
- <a href="1998/bangerth.bib" target="body">BibTeX entry</a>)
</li>
</ol>