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Interpolation of non-smooth functions on anisotropic finite element meshesApel, Th. 30 October 1998 (has links) (PDF)
In this paper, several modifications of the quasi-interpolation operator
of Scott and Zhang (Math. Comp. 54(1990)190, 483--493) are discussed.
The modified operators are defined for non-smooth functions and are suited
for the application on anisotropic meshes. The anisotropy of the elements
is reflected in the local stability and approximation error estimates.
As an application, an example is considered where anisotropic finite element
meshes are appropriate, namely the Poisson problem in domains with edges.
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Elliptic problems in domains with edges: anisotropic regularity and anisotropic finite element meshesApel, T., Nicaise, S. 30 October 1998 (has links) (PDF)
This paper is concerned with the anisotropic singular behaviour of the solution of elliptic boundary value problems near edges. The paper deals first with the description of the analytic properties of the solution in newly defined, anisotropically weighted Sobolev spaces. The finite element method with anisotropic, graded meshes and piecewise linear shape functions is then investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates in anisotropically weighted spaces are derived. Moreover, it is shown that the condition number of the stiffness matrix is not affected by the mesh grading. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones.
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A parallel version of the preconditioned conjugate gradient method for boundary element equationsPester, M., Rjasanow, S. 30 October 1998 (has links) (PDF)
The parallel version of precondition techniques is developed for
matrices arising from the Galerkin boundary element method for
two-dimensional domains with Dirichlet boundary conditions.
Results were obtained for implementations on a transputer network
as well as on an nCUBE-2 parallel computer showing that iterative
solution methods are very well suited for a MIMD computer. A
comparison of numerical results for iterative and direct solution
methods is presented and underlines the superiority of iterative
methods for large systems.
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Realization and comparison of various mesh refinement strategies near edgesApel, T., Milde, F. 30 October 1998 (has links) (PDF)
This paper is concerned with mesh refinement techniques for
treating elliptic boundary value problems in domains with re-
entrant edges and corners, and focuses on numerical experiments.
After a section about the model problem and discretization
strategies, their realization in the experimental code FEMPS3D is
described. For two representative examples the numerically
determined error norms are recorded, and various mesh refinement
strategies are compared.
|
5 |
Elliptic problems in domains with edges: anisotropic regularity and anisotropic finite element meshesApel, T., Nicaise, S. 30 October 1998 (has links)
This paper is concerned with the anisotropic singular behaviour of the solution of elliptic boundary value problems near edges. The paper deals first with the description of the analytic properties of the solution in newly defined, anisotropically weighted Sobolev spaces. The finite element method with anisotropic, graded meshes and piecewise linear shape functions is then investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates in anisotropically weighted spaces are derived. Moreover, it is shown that the condition number of the stiffness matrix is not affected by the mesh grading. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones.
|
6 |
Interpolation of non-smooth functions on anisotropic finite element meshesApel, Th. 30 October 1998 (has links)
In this paper, several modifications of the quasi-interpolation operator
of Scott and Zhang (Math. Comp. 54(1990)190, 483--493) are discussed.
The modified operators are defined for non-smooth functions and are suited
for the application on anisotropic meshes. The anisotropy of the elements
is reflected in the local stability and approximation error estimates.
As an application, an example is considered where anisotropic finite element
meshes are appropriate, namely the Poisson problem in domains with edges.
|
7 |
A parallel version of the preconditioned conjugate gradient method for boundary element equationsPester, M., Rjasanow, S. 30 October 1998 (has links)
The parallel version of precondition techniques is developed for
matrices arising from the Galerkin boundary element method for
two-dimensional domains with Dirichlet boundary conditions.
Results were obtained for implementations on a transputer network
as well as on an nCUBE-2 parallel computer showing that iterative
solution methods are very well suited for a MIMD computer. A
comparison of numerical results for iterative and direct solution
methods is presented and underlines the superiority of iterative
methods for large systems.
|
8 |
Realization and comparison of various mesh refinement strategies near edgesApel, T., Milde, F. 30 October 1998 (has links)
This paper is concerned with mesh refinement techniques for
treating elliptic boundary value problems in domains with re-
entrant edges and corners, and focuses on numerical experiments.
After a section about the model problem and discretization
strategies, their realization in the experimental code FEMPS3D is
described. For two representative examples the numerically
determined error norms are recorded, and various mesh refinement
strategies are compared.
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