Conforming P3 Divergence-Free Finite Elements for the Stokes Equations on Subquadrilateral Triangular Meshes

doi:10.1007/s42967-023-00335-0

Abstract

Abstract: 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.

Key words: Divergence-free, Stokes equations, Finite element, Triangular mesh, Quadrilateral mesh

CLC Number:

65N15
65N30

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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References

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Conforming P₃ Divergence-Free Finite Elements for the Stokes Equations on Subquadrilateral Triangular Meshes

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