Anisotropic pressure-robust discretizations for the Navier-Stokes equations
Anisotropic pressure-robust discretizations for the Navier-Stokes equations
Supervision:
Development:
Goals:
- A priori error estimates for pressure-robust discretizations of the Navier-Stokes equations on anisotropic meshes
- Verification of the theoretical results through numerical tests
Students works related to the project:
- Böhme, W.: Finite-Elemente-Netze ohne Maximalwinkelbedingung in dreidimensionalen Gebieten, Masterarbeit, UniBw München 2020.
- Böhme, W.: Implementierung eines a-posteriori Fehlerschätzers für die Stokes Gleichungen, Projektarbeit, UniBw München, 2019.
- Böhme, W.: Finite-Elemente-Lösung einer Randwertaufgabe mit nichtglatter Randbedingung, Bachelorarbeit, UniBw München, 2019.
Publications related to the project:
- Kempf, V.: Pressure-robustness for the Stokes equations on anisotropic meshes, Proceedings in Applied Mathematics and Mechanics, 21(1):e202100112, DOI: 10.1002/pamm.202100112
- Apel, T.; Kempf, V.: Pressure-robust error estimate of optimal order for the Stokes equations: domains with re-entrant edges and anisotropic mesh grading, Calcolo, 58(2):15, DOI: 10.1007/s10092-021-00402-zarXiv
- Apel, T.; Kempf, V.; Linke, A.; Merdon, C.: A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes, IMA Journal of Numerical Analysis, 42(1):392-416, DOI: 10.1093/imanum/draa097 arXiv
- Apel, T.; Kempf, V.: Brezzi--Douglas--Marini interpolation of any order on anisotropic triangles and tetrahedra, SIAM Journal on Numerical Analysis, 58(3):1696-1718, DOI: 10.1137/19M1302910 arXiv