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A Posteriori Error Estimates For The Stokes Problem (1991)
| Content Provider | CiteSeerX |
|---|---|
| Author | Bank, Randolph E. Bruno Welfert, Bruno D. |
| Abstract | . We derive and analyze an a posteriori error estimate 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 \Theta 9 system which reduces to two 3 \Theta 3 systems easily invertible. Comparisons with other estimates based on a Petrov-Galerkin solution are used in our 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. Key words. Mixed finite element methods, Stokes equations, a posteriori error estimates, mesh adaptation, mini-element formulation, Petrov-Galerkin formulation. AMS subject classifications. 65F10, 65N20, 65N30. 1. Introduction. The need for accurate solutions of large scal... |
| File Format | |
| Volume Number | 28 |
| Journal | SIAM J. Numer. Anal |
| Language | English |
| Publisher Date | 1991-01-01 |
| Access Restriction | Open |
| Subject Keyword | Posteriori Error Estimate Stokes Problem Stokes Equation Quadratic Bump Function Accurate Solution Numerical Experiment Local Stokes Problem Am Subject Classification Reasonable Approximation Finite Element Mesh Mini-element Discretization Petrov-galerkin Solution Actual Discretization Error Mini-element Formulation Mesh Adaptation Self Adaptive Mesh Refinement Procedure Petrov-galerkin Formulation Pressure Error Mixed Finite Element Method Key Word |
| Content Type | Text |
| Resource Type | Article |
