The continuous P3 and discontinuous P2 finite element pair is stable on subquadrilateral triangular meshes for solving 2D stationary Stokes equations. By putting two diagonal lines into every quadrilateral of a quadrilateral mesh, we get a subquadrilateral triangular mesh. Such a velocity solution is divergence-free point wise and viscosity robust in the sense the solution and the error are independent of the viscosity. Numerical examples show an advantage of such a method over the Taylor-Hood P3-P2 method, where the latter deteriorates when the viscosity becomes small.
Shangyou Zhang
. Conforming P3 Divergence-Free Finite Elements for the Stokes Equations on Subquadrilateral Triangular Meshes[J]. Communications on Applied Mathematics and Computation, 2025
, 7(2)
: 426
-441
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DOI: 10.1007/s42967-023-00335-0
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