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+<!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">
+ <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+ <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">
+ <link href="../../print.css" rel="StyleSheet" media="print">
+ <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">
+ <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+ <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">
+ <link href="../../print.css" rel="StyleSheet" media="print">
+ <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">
+ <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+ <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">
+ <link href="../../print.css" rel="StyleSheet" media="print">
+ <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//EN"
+ "http://www.w3.org/TR/REC-html40/strict.dtd">
+<html>
+ <head>
+ <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
+ <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+ <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">
+ <link href="../../print.css" rel="StyleSheet" media="print">
+ <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">
+ <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+ <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">
+ <link href="../../print.css" rel="StyleSheet" media="print">
+ <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>
+ <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
+ <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+ <body>
+ <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>