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.202100112doi.png
  • 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-zdoi.pngarXiv web-logo.png
  • 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/draa097doi.png arXiv web-logo.png
  • 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: 10.1137/19M1302910doi.png arXiv web-logo.png