On the initial higher-order pressure convergence in equal-order finite element discretizations of the Stokes system

Douglas R.Q. Pacheco*, Olaf Steinbach

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In incompressible flow problems, the finite element discretization of pressure and velocity can be done through either stable spaces or stabilized pairs. For equal-order stabilized methods with piecewise linear discretization, the classical theory guarantees only linear convergence for the pressure approximation. However, a higher order is often observed, yet seldom discussed, in numerical practice. Such experimental observations may, in the absence of a sound a priori error analysis, mislead the selection of finite element spaces in practical applications. Therefore, we present here a numerical analysis demonstrating that an initial higher-order pressure convergence may in fact occur under certain conditions, for equal-order elements of any degree. Moreover, our numerical experiments clearly indicate that whether and for how long this behavior holds is a problem-dependent matter. These findings confirm that an optimal pressure convergence can in general not be expected when using unbalanced velocity-pressure pairs.

Original languageEnglish
Pages (from-to)140-145
Number of pages6
JournalComputers and Mathematics with Applications
Volume109
DOIs
Publication statusPublished - 1 Mar 2022

Keywords

  • Finite element methods
  • Incompressible flow
  • Numerical analysis
  • Stabilized finite element methods
  • Stokes system
  • Superconvergence

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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