Stabilization arising from PGEM: A review and further developments

doi:10.1016/j.apnum.2008.12.004

Applied Numerical Mathematics

Volume 59, Issue 9, September 2009, Pages 2065-2081

https://doi.org/10.1016/j.apnum.2008.12.004 Get rights and content

Abstract

The aim of this paper is twofold. First, we review the recent Petrov–Galerkin enriched method (PGEM) to stabilize numerical solutions of BVP's in primal and mixed forms. Then, we extend such enrichment technique to a mixed singularly perturbed problem, namely, the generalized Stokes problem, and focus on a stabilized finite element method arising in a natural way after performing static condensation. The resulting stabilized method is shown to lead to optimal convergences, and afterward, it is numerically validated.

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¹: This author is partially supported by FONDECYT Project No. 1070698.

²: This author is partially supported by CONICYT-Chile through FONDECYT Project No. 1061032 and FONDAP Program on Applied Mathematics.

³: Present address: Department of Mathematics, University of Strathclyde, 26 Richmond street, Glasgow G1 1XH, UK

⁴: This author is partially supported by NSF Grant No. 0610039.

⁵: This author is supported by CNPq grant No. 304051/2006-3 and FAPERJ.

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Stabilization arising from PGEM: A review and further developments

Abstract

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

C. R. Math. Acad. Sci. Paris, Ser.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

J. Math. Anal. Appl.

Stabilized finite element methods based on multiscale enrichment for the Stokes problem

SIAM J. Numer. Anal.

A stabilized finite element method for the Stokes problem including element and edge residuals

IMA J. Numer. Anal.