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) |
|---|---|
| Pages (from-to) | 591-623 |
| Number of pages | 33 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 28 |
| Issue number | 3 |
| State | Published - Jun 1991 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
- Computational Mathematics
Cite this
Posteriori error estimates for the Stokes problem. / Bank, Randolph E.; Welfert, Bruno.
In: SIAM Journal on Numerical Analysis, Vol. 28, No. 3, 06.1991, p. 591-623.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Posteriori error estimates for the Stokes problem
AU - Bank, Randolph E.
AU - Welfert, Bruno
PY - 1991/6
Y1 - 1991/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0026173586&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0026173586&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0026173586
VL - 28
SP - 591
EP - 623
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
SN - 0036-1429
IS - 3
ER -