An SPD stabilized finite element method for the Stokes equations

Huoyuan Duan, Roger C.E. Tan, Suh Yuh Yang, Cheng Shu You

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A new residual-based stabilized finite element method is analysed for solving the Stokes equations in terms of velocity and pressure, where the H-1 norm is introduced in the measurement of the residuals to obtain a symmetric positive-definite method. The H-1 norm is computable and can always be easily realized offline by the continuous linear finite element solution or the preconditioner counterpart of the Poisson Dirichlet problem. Although the H-1 norm is computed in the linear element space, no matter what the finite element spaces for the velocity and the pressure are, optimal error bounds can be established when using continuous finite element pairs Rl-Rm for velocity and pressure for any l,m ≥ 1. Numerical experiments are performed to confirm the theoretical results obtained.

Original languageEnglish
Pages (from-to)1812-1841
Number of pages30
JournalIMA Journal of Numerical Analysis
Volume35
Issue number4
DOIs
StatePublished - 24 Feb 2014

Keywords

  • H norm
  • Stokes equations
  • linear finite element solution of the Poisson Dirichlet problem
  • stabilized finite element method
  • symmetric positivedefiniteness

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