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 - P1 disc element applied to the 3D stationary Stokes and Navier-Stokes problem, respectively. Moreover, applying a Q3 - P2 disc 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 - P1 disc discretization, and the Q 3 - P2 disc 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 2005
Externally publishedYes

Fingerprint

Navier-Stokes Problem
Superconvergence
Interpolants
Stokes
Discretization
Finite Element Method
Third-order Method
Cost-benefit Analysis
Finite element method
Discretization Error
Finite Element Solution
Poisson's equation
Boundary Value
Post-processing
Lagrange
Piecewise Linear
Convergence Properties
Convergence Rate
Interpolate
Numerical Experiment

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

Superconvergence of a 3D finite element method for stationary Stokes and Navier-Stokes problems. / Matthies, G.; Skrzypacz, P.; Tobiska, L.

In: Numerical Methods for Partial Differential Equations, Vol. 21, No. 4, 07.2005, p. 701-725.

Research output: Contribution to journalArticle

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