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 language | English |
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Pages (from-to) | 701-725 |
Number of pages | 25 |
Journal | Numerical Methods for Partial Differential Equations |
Volume | 21 |
Issue number | 4 |
DOIs | |
Publication status | Published - Jul 1 2005 |
Keywords
- Finite elements
- Navier-Stokes equations
- Postprocessing
- Superconvergence
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics