Inf-sup stability of the trace P_2-P_1 Taylor-Hood elements for surface PDEs

09/06/2019
by   Maxim A. Olshanskii, et al.
0

The paper studies a geometrically unfitted finite element method (FEM), known as trace FEM or cut FEM, for the numerical solution of the Stokes system posed on a closed smooth surface. A trace FEM based on standard Taylor-Hood (continuous P_2-P_1) bulk elements is proposed. A so-called volume normal derivative stabilization, known from the literature on trace FEM, is an essential ingredient of this method. The key result proved in the paper is an inf-sup stability of the trace P_2-P_1 finite element pair, with the stability constant uniformly bounded with respect to the discretization parameter and the position of the surface in the bulk mesh. Optimal order convergence of a consistent variant of the finite element method follows from this new stability result and interpolation properties of the trace FEM. Properties of the method are illustrated with numerical examples.

READ FULL TEXT
research
09/06/2019

Inf-sup stability of the trace P2-P1 Taylor-Hood elements for surface PDEs

The paper studies a geometrically unfitted finite element method (FEM), ...
research
05/11/2023

Finite element approximation of unique continuation of functions with finite dimensional trace

We consider a unique continuation problem where the Dirichlet trace of t...
research
06/01/2023

A scalar auxiliary variable unfitted FEM for the surface Cahn-Hilliard equation

The paper studies a scalar auxiliary variable (SAV) method to solve the ...
research
01/04/2021

Optimization and variational principles for the shear strength reduction method

This paper is focused on the definition, analysis and numerical solution...
research
07/18/2020

A finite element method for Allen-Cahn equation on deforming surface

The paper studies an Allen-Cahn-type equation defined on a time-dependen...
research
04/24/2023

Analysis of a FEM-MCM Discretization for the 2D/3D stochastic closed-loop geothermal system

This paper develops a new 2D/3D stochastic closed-loop geothermal system...
research
02/26/2020

Bulk-surface virtual element method for systems of coupled bulk-surface PDEs in two-space dimensions

In this manuscript we present a novel bulk-surface virtual element metho...

Please sign up or login with your details

Forgot password? Click here to reset