Superconvergence of a 3D finite element method for stationary Stokes and Navier-Stokes problems

G. Matthies, P. Skrzypacz, L. Tobiska

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

For the Poisson equation on rectangular and brick meshes it is well known that the piecewise linear conforming finite element solution approximates the interpolant to a higher order than the solution itself. In this article, this type of supercloseness property is established for a special interpolant of the Q2 - P1disc element applied to the 3D stationary Stokes and Navier-Stokes problem, respectively. Moreover, applying a Q3 - P2disc postprocessing technique, we can also state a superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself. Finally, we show that inhomogeneous boundary values can be approximated by the Lagrange Q 2-interpolation without influencing the super-convergence property. Numerical experiments verify the predicted convergence rates. Moreover, a cost-benefit analysis between the two third-order methods, the post-processed Q2 - P1disc discretization, and the Q 3 - P2disc discretization is carried out.

Original languageEnglish
Pages (from-to)701-725
Number of pages25
JournalNumerical Methods for Partial Differential Equations
Volume21
Issue number4
DOIs
Publication statusPublished - Jul 1 2005

Keywords

  • Finite elements
  • Navier-Stokes equations
  • Postprocessing
  • Superconvergence

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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