Equal Order Discontinuous Finite Volume Element Methods for the Stokes Problem

Sarvesh Kumar, Ricardo Ruiz-Baier

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16 Citations (Scopus)

Abstract

The aim of this paper is to develop and analyze a family of stabilized discontinuous finite volume element methods for the Stokes equations in two and three spatial dimensions. The proposed scheme is constructed using a baseline finite element approximation of velocity and pressure by discontinuous piecewise linear elements, where an interior penalty stabilization is applied. A priori error estimates are derived for the velocity and pressure in the energy norm, and convergence rates are predicted for velocity in the $$L^2$$L2-norm under the assumption that the source term is locally in $$ H^1$$H1. Several numerical experiments in two and three spatial dimensions are presented to validate our theoretical findings.

Original languageEnglish
Pages (from-to)956-978
Number of pages23
JournalJournal of Scientific Computing
Volume65
Issue number3
DOIs
Publication statusPublished - 6 Feb 2015
Externally publishedYes

Keywords

  • Discontinuous Galerkin methods
  • Error analysis
  • Finite volume element methods
  • Stabilization
  • Stokes equations

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