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- Title
A stable and H1-conforming divergence-free finite element pair for the Stokes problem using isoparametric mappings.
- Authors
Neilan, Michael; Otus, M. Baris
- Abstract
This paper expands the isoparametric framework to construct a stable, H 1 -conforming, and divergence-free method for the Stokes problem in two dimensions based on the Scott-Vogelius pair on Clough-Tocher splits. The pressure space is defined through composition, whereas the velocity space is constructed via a new divergence-preserving mapping that imposes full continuity across shared edges in the isoparametric mesh. Our construction is motivated by operators and spaces found in isoparametric C 1 finite element methods. We prove the method is stable, pressure-robust, and has optimal order convergence. Numerical experiments are provided which confirm the theoretical results.
- Subjects
FINITE element method; STOKES equations; BASE pairs
- Publication
Calcolo, 2023, Vol 60, Issue 3, p1
- ISSN
0008-0624
- Publication type
Article
- DOI
10.1007/s10092-023-00531-7