A posteriori error estimation for convection-dominated problems
| Thesis title in Czech: | Aposteriorní odhady chyby pro úlohy s dominantní konvekcí |
|---|---|
| Thesis title in English: | A posteriori error estimation for convection-dominated problems |
| Key words: | a posteriorní odhady chyby|dominantní konvekce|metoda konečných prvků |
| English key words: | a posteriori error estimation|dominant convection|finite element method |
| Academic year of topic announcement: | 2024/2025 |
| Thesis type: | dissertation |
| Thesis language: | angličtina |
| Department: | Department of Numerical Mathematics (32-KNM) |
| Supervisor: | doc. Mgr. Petr Knobloch, Dr., DSc. |
| Author: |
| Guidelines |
| In many physical situations convective effects play a dominant role, which causes severe difficulties in numerical simulations. A typical but still difficult model problem is a convection-diffusion equation which will be considered also in this work. To estimate errors of approximate solutions to convection-diffusion problems and to drive a refinement process, various a posteriori error estimators have been developed. Although many results have been published in the literature, several important open problems still remain unsolved in the convection-dominated regime. In particular, it is desirable to derive a posteriori error estimates with respect to more appropriate norms than used in the literature, further research is needed in designing and analyzing a posteriori estimators for nonlinear schemes, and also a posteriori error estimation for methods using anisotropic meshes has to be further developed and analyzed. The thesis should compare various a posteriori error estimators for finite element discretizations of convection-diffusion equations and contribute to the clarification of some of the open problems. |
| References |
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