Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Pressure-improved Scott-Vogelius type elements

Nis-Erik Bohne, Benedikt Gräßle, Stefan A. Sauter

Abstract

The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximation. However, it is well known that the convergence rates for the discrete pressure deteriorate in the presence of certain $critical$ $vertices$ in a triangulation of the domain. Modifications of the Scott-Vogelius element such as the recently introduced pressure-wired Stokes element also suffer from this effect. In this paper we introduce a simple modification strategy for these pressure spaces that preserves the inf-sup stability while the pressure converges at an optimal rate.

Pressure-improved Scott-Vogelius type elements

Abstract

The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximation. However, it is well known that the convergence rates for the discrete pressure deteriorate in the presence of certain in a triangulation of the domain. Modifications of the Scott-Vogelius element such as the recently introduced pressure-wired Stokes element also suffer from this effect. In this paper we introduce a simple modification strategy for these pressure spaces that preserves the inf-sup stability while the pressure converges at an optimal rate.
Paper Structure (4 sections, 15 equations, 1 figure)

This paper contains 4 sections, 15 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Stokes problem and its numerical discretization
  3. Pressure improved Scott-Vogelius element
  4. The Scott-Vogelius element

Figures (1)

  • Figure 1: Vertex patch for an interior singular vertex $\mathbf{z}\in\mathcal{V}_{\Omega}(\mathcal{T})$ with $N_{\mathbf{z}}=4$ (resp. boundery singular vertex $\mathbf{z}\in\mathcal{V}_{\partial\Omega }(\mathcal{T})$ with $N_{\mathbf{z}}=1,2,3$) triangles

Theorems & Definitions (1)

  • Definition 3.1