Development and analysis of monotone numerical schemes
| Thesis title in Czech: | Vývoj a analýza monotónních numerických schémat |
|---|---|
| Thesis title in English: | Development and analysis of monotone numerical schemes |
| Key words: | cross diffusion|existence of solutions|FE-FCT stabilization methods|positivity preservation |
| English key words: | cross diffusion|existence of solutions|FE-FCT stabilization methods|positivity preservation |
| Academic year of topic announcement: | 2017/2018 |
| Thesis type: | dissertation |
| Thesis language: | angličtina |
| Department: | Department of Numerical Mathematics (32-KNM) |
| Supervisor: | prof. Mgr. Petr Knobloch, Dr., DSc. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 27.09.2018 |
| Date of assignment: | 27.09.2018 |
| Confirmed by Study dept. on: | 29.10.2018 |
| Date and time of defence: | 06.11.2024 10:45 |
| Date of electronic submission: | 15.07.2024 |
| Date of submission of printed version: | 15.07.2024 |
| Date of proceeded defence: | 06.11.2024 |
| Opponents: | Dr. Matthias Möller |
| doc. RNDr. Petr Sváček, Ph.D. | |
| Guidelines |
| The aim of the thesis is to develop and analyze monotone discretizations of problems of the mathematical physics. A typical example are convection-diffusion-reaction equations or transport problems, nevertheless the research may cover also other problem classes. An important part will also be an efficient numerical solution of the discrete problems which are often nonlinear. |
| References |
| Recommended literature:
T. Ikeda: Maximum principle in finite element models for convection-diffusion phenomena, North-Holland, Amsterdam, 1983. D. Kuzmin: A guide to numerical methods for transport equations, Friedrich-Alexander-Universität Erlangen-Nürnberg, 2010. M.H. Protter, H.F. Weinberger: Maximum principles in differential equations, Springer, New York, 1984. P. Pucci, J. Serrin: The maximum principle, Birkhäuser, Basel, 2007. H.-G. Roos, M. Stynes, L. Tobiska: Robust numerical methods for singularly perturbed differential equations, Springer, Berlin, 2008. T. Vejchodský: Discrete maximum principles, Habilitation Thesis, Charles University in Prague, 2011. journal literature provided by the supervisor |