Abstract
An a posteriori error estimate is derived and analyzed for the mini-element discretization of the Stokes equations. The estimate is based on the solution of a local Stokes problem in each element of the finite element mesh, using spaces of quadratic bump functions for both velocity and pressure errors. This results in solving a 9 × 9 system which reduces to two easily invertible 3 × 3 systems. Comparisons with other estimates based on a Petrov-Galerkin solution are used in this analysis, which shows that it provides a reasonable approximation of the actual discretization error. Numerical experiments clearly show the efficiency of such an estimate in the solution of self-adaptive mesh refinement procedures.
Original language | English (US) |
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Pages (from-to) | 591-623 |
Number of pages | 33 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 28 |
Issue number | 3 |
DOIs | |
State | Published - 1991 |
Externally published | Yes |
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics