From 1e06dd03cd5e36a4189257499bb46b9005e25d3d Mon Sep 17 00:00:00 2001 From: hartmann Date: Mon, 6 Jun 2005 16:01:33 +0000 Subject: [PATCH] Update of references. git-svn-id: https://svn.dealii.org/trunk@10842 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/doc/publications/2002/har02.bib | 20 ++++++ deal.II/doc/publications/2002/har02.html | 91 ++++++++++++++++++++++++ deal.II/doc/publications/2002/hh02a.bib | 21 ++++++ deal.II/doc/publications/2002/hh02a.html | 39 ++++++++++ deal.II/doc/publications/2002/hh02b.bib | 22 ++++++ deal.II/doc/publications/2002/hh02b.html | 39 ++++++++++ deal.II/doc/publications/2003/hh03a.bib | 20 ++++++ deal.II/doc/publications/2003/hh03a.html | 28 ++++++++ deal.II/doc/publications/2003/hh03b.bib | 20 ++++++ deal.II/doc/publications/2003/hh03b.html | 43 +++++++++++ deal.II/doc/publications/2004/hh04a.bib | 21 ++++++ 11 files changed, 364 insertions(+) create mode 100644 deal.II/doc/publications/2002/har02.bib create mode 100644 deal.II/doc/publications/2002/har02.html create mode 100644 deal.II/doc/publications/2002/hh02a.bib create mode 100644 deal.II/doc/publications/2002/hh02a.html create mode 100644 deal.II/doc/publications/2002/hh02b.bib create mode 100644 deal.II/doc/publications/2002/hh02b.html create mode 100644 deal.II/doc/publications/2003/hh03a.bib create mode 100644 deal.II/doc/publications/2003/hh03a.html create mode 100644 deal.II/doc/publications/2003/hh03b.bib create mode 100644 deal.II/doc/publications/2003/hh03b.html create mode 100644 deal.II/doc/publications/2004/hh04a.bib diff --git a/deal.II/doc/publications/2002/har02.bib b/deal.II/doc/publications/2002/har02.bib new file mode 100644 index 0000000000..4ff32c921f --- /dev/null +++ b/deal.II/doc/publications/2002/har02.bib @@ -0,0 +1,20 @@ + + + + + + +

+
+@PhdThesis{Har02,
+  author = 	 {Ralf Hartmann},
+  title = 	 {Adaptive Finite Element Methods for the
+                  Compressible Euler Equations},
+  school = 	 {University of Heidelberg},
+  year = 	 2002
+}
+
+
+
+

diff --git a/deal.II/doc/publications/2002/har02.html b/deal.II/doc/publications/2002/har02.html new file mode 100644 index 0000000000..83d15611ec --- /dev/null +++ b/deal.II/doc/publications/2002/har02.html @@ -0,0 +1,91 @@ + + + + + + + + +

Abstract:

+ +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 a posteriori 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. +
+
+In particular, this work includes following issues +

+ Discretisation: +
- Streamline diffusion and discontinuous Galerkin method + for a scalar hyperbolic problem:
  comparison with respect to + accuracy and conservation properties +
- Discontinuous Galerkin method for the compressible Euler equations +
- Use of shock-capturing +
- Higher order boundary approximation at reflective boundaries +
- Solution of the nonlinear and the linear problems +
- Mesh generation for airfoil computations +
+
+ +
+ A posteriori error estimation and adaptivity: +
- Derivation (by duality argument) of error estimates with + respect to arbitrary target functionals + +
- Question of well-posedness of the dual problem + +
- Approximation of the error representation by numerical + approximation of the dual solution + +
- Adaptive algorithm tailored to the efficient computation + of the quantity of interest +
+
+ +
Numerical Examples illustrating the performance of the + error estimation and the adaptive grid refinement for a wide range + of hyperbolic problems including +
- the linear advection equation +
- the 1D inviscid Burgers equation +
- the Buckley-Leverett equation +
- the 1D compressible Euler equations +
- and several examples for the 2D compressible Euler equations. +
+ and for a variety of target functionals (quantities) including +
- drag and lift coefficients of airfoils +
- pressure point values +
- weighted boundary integrals +
+
+ +
+ Appendices +
- Full description of exact solutions to hyperbolic + problems treated in numerical examples + +
- Implementational details of finite elements with curved + boundaries + +
+

+ + + + + diff --git a/deal.II/doc/publications/2002/hh02a.bib b/deal.II/doc/publications/2002/hh02a.bib new file mode 100644 index 0000000000..987d5f6c0f --- /dev/null +++ b/deal.II/doc/publications/2002/hh02a.bib @@ -0,0 +1,21 @@ + + + + + + +

+
+@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}
+}
+
+
+

diff --git a/deal.II/doc/publications/2002/hh02a.html b/deal.II/doc/publications/2002/hh02a.html new file mode 100644 index 0000000000..bfd77c63b5 --- /dev/null +++ b/deal.II/doc/publications/2002/hh02a.html @@ -0,0 +1,39 @@ + + + + + + + + +

Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws

+R. Hartmann and P. Houston + + +

Abstract:

+ +We consider the a posteriori 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 +a posteriori 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 a posteriori +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 +ad hoc error indicators. + + + + diff --git a/deal.II/doc/publications/2002/hh02b.bib b/deal.II/doc/publications/2002/hh02b.bib new file mode 100644 index 0000000000..1a7a7c4941 --- /dev/null +++ b/deal.II/doc/publications/2002/hh02b.bib @@ -0,0 +1,22 @@ + + + + + + +

+
+
+@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}
+}
+
+

diff --git a/deal.II/doc/publications/2002/hh02b.html b/deal.II/doc/publications/2002/hh02b.html new file mode 100644 index 0000000000..f5eab49833 --- /dev/null +++ b/deal.II/doc/publications/2002/hh02b.html @@ -0,0 +1,39 @@ + + + + + + + +

Adaptive Discontinuous Galerkin Finite Element Methods for the Compressible Euler Equations

+R. Hartmann and P. Houston + +

Abstract:

+ +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 a posteriori 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 + ad hoc 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. + + + + diff --git a/deal.II/doc/publications/2003/hh03a.bib b/deal.II/doc/publications/2003/hh03a.bib new file mode 100644 index 0000000000..da78e6a12b --- /dev/null +++ b/deal.II/doc/publications/2003/hh03a.bib @@ -0,0 +1,20 @@ + + + + + + +

+
+@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}
+}
+
+

diff --git a/deal.II/doc/publications/2003/hh03a.html b/deal.II/doc/publications/2003/hh03a.html new file mode 100644 index 0000000000..5d650a7ac5 --- /dev/null +++ b/deal.II/doc/publications/2003/hh03a.html @@ -0,0 +1,28 @@ + + + + + + + +

Goal-Oriented A Posteriori Error Estimation for Compressible Fluid Flows

+R. Hartmann and P. Houston + + +

Abstract:

+ +

+ We consider so-called `goal-oriented' a posteriori 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, a + posteriori 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. +

+ + + diff --git a/deal.II/doc/publications/2003/hh03b.bib b/deal.II/doc/publications/2003/hh03b.bib new file mode 100644 index 0000000000..fbf45fd13f --- /dev/null +++ b/deal.II/doc/publications/2003/hh03b.bib @@ -0,0 +1,20 @@ + + + + + + +

+
+@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},
+}
+
+

diff --git a/deal.II/doc/publications/2003/hh03b.html b/deal.II/doc/publications/2003/hh03b.html new file mode 100644 index 0000000000..0627d3f5f7 --- /dev/null +++ b/deal.II/doc/publications/2003/hh03b.html @@ -0,0 +1,43 @@ + + + + + + + +

Goal-Oriented A Posteriori Error Estimation for Multiple Target Functionals

+R. Hartmann and P. Houston + + +

Abstract:

+ +

+ 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. +
+ In a series of previous articles, we have developed the theory of + goal--oriented a posteriori error estimation for + discontinuous Galerkin methods applied to inviscid compressible + fluid flows. On the basis of Type I a posteriori 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 single target functional of + practical interest. The purpose of the current article is to extend + this earlier work to the case when several target + functionals of the solution need to be simultaneously approximated + to a given level of accuracy. +

+ + + diff --git a/deal.II/doc/publications/2004/hh04a.bib b/deal.II/doc/publications/2004/hh04a.bib new file mode 100644 index 0000000000..da9e21b0fe --- /dev/null +++ b/deal.II/doc/publications/2004/hh04a.bib @@ -0,0 +1,21 @@ + + + + + + +

+
+@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
+}
+
+

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