Stabilization arising from PGEM: A review and further developments

被引：15
作者：
Araya, Rodolfo [1 ]
Barrenechea, Gabriel R. [1 ]
Franca, Leopoldo P. [2 ]
Valentin, Frederic [3 ]
机构：
[1] Univ Concepcion, Dept Ingn Matemat, Concepcion, Chile
[2] Univ Colorado, Dept Math, Denver, CO 80217 USA
[3] Lab Nacl Comp Cient, Dept Matemat Aplicada, BR-25651070 Petropolis, RJ, Brazil
来源：
APPLIED NUMERICAL MATHEMATICS | 2009年 / 59卷 / 09期
基金：
美国国家科学基金会;
关键词：
Stokes operator; Reactive flow; Multiscale function; Petrov-Galerkin method; Stabilization; FINITE-ELEMENT METHODS; COMPUTATIONAL FLUID-DYNAMICS; PETROV-GALERKIN FORMULATIONS; STOKES PROBLEM; MULTISCALE ENRICHMENT; BUBBLES; APPROXIMATION;
D O I：
10.1016/j.apnum.2008.12.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：2065 / 2081
页数：17
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