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

✍ Scribed by G. Matthies; P. Skrzypacz; L. Tobiska

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 201 KB
• Volume: 21
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.20058

✦ Synopsis

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 Q~2~ − P element applied to the 3D stationary Stokes and Navier‐Stokes problem, respectively. Moreover, applying a Q~3~ − P 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 superconvergence property. Numerical experiments verify the predicted convergence rates. Moreover, a cost‐benefit analysis between the two third‐order methods, the post‐processed Q~2~ − P discretization, and the Q~3~ − P discretization is carried out. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005