Add support for the Conforming Crouzeix-Raviart Element for Stokes
The conforming Crouzeix-Raviart element P_2^+-P_1^\text{disc}
is a stable mixed pairing for discretising the Stokes and associated problems, see e.g.
- M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations I, Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique, 1973, 7, 33-75
- Rolf Krahl and Eberhard Bänsch, Computational Comparison between the Taylor-Hood and the Conforming Crouzeix-Raviart element, Proceedings of ALGORITMY 2005, 2005, 369-379
- Cedric Thieulot and Wolfgang Bangerth, On the choice of finite element for applications in geodynamics. Part II: A comparison of simplex and hypercube elements, 2024, preprint
Our plan is to support generation of forms and operators for the P_2^+-P_1^\text{disc}
pair. Initially we will only consider the case of
triangles in 2D. Here the P_2^+
part for the velocity component employs continuous quadratic Lagrange elements extended by a cubic bubble function.
-
implement a P2PlusBubbleSpace
in HOG to supportP_2^+
-
add support for generating forms and operators using P_2^+
elements; especially diffusion operators -
add support for DG1 elements to allow using P_1^\text{disc}
-
implement form generation for divergence and gradient parts using the P_2^+-P_1^\text{disc}
pair -
implement operator generation for divergence and gradient parts using the P_2^+-P_1^\text{disc}
pair
Operator generation for the mixed pair will require more work as it necessitates extending the concept of an elementwise operator to DG, see #19. Note, however, that our case here is simpler, as we do only need volume integrals and do not have flux coupling or anything like that.
Edited by Marcus Mohr