hp-finite element simulations for Stokes flow -: stable and stabilized

被引：18
作者：
Gerdes, K [1 ]
Schötzau, D
机构：
[1] Chalmers Univ Technol, Dept Math, SE-41296 Gothenburg, Sweden
[2] ETH Zurich, Seminar Angew Math, CH-8092 Zurich, Switzerland
来源：
FINITE ELEMENTS IN ANALYSIS AND DESIGN | 1999年 / 33卷 / 03期
关键词：
hp-FEM; Stokes problem; Galerkin formulation; Galerkin least squares formulation;
D O I：
10.1016/S0168-874X(99)00018-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The stable Galerkin formulation and a stabilized Galerkin least squares formulation for the Stokes problem are analyzed in the context of the hp-version of the finite element method. Theoretical results for both formulations establish exponential rates of convergence under realistic assumptions on the input data. We confirm these results by a series of numerical experiments on an L-shaped domain where the solution exhibits corner singularities. (C) 1999 Elsevier Science B.V. All rights reserved. AMS classification: 65N30; 65N35; 65N50.
引用
收藏
页码：143 / 165
页数：23
相关论文
共 43 条
[1]   A posteriori error estimators for the Stokes and Oseen equations [J].
Ainsworth, M ;
Oden, JT .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (01) :228-245
[2]   THE OPTIMAL CONVERGENCE RATE OF THE P-VERSION OF THE FINITE-ELEMENT METHOD [J].
BABUSKA, I ;
SURI, M .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (04) :750-776
[3]   REGULARITY OF THE SOLUTION OF ELLIPTIC PROBLEMS WITH PIECEWISE ANALYTIC DATA .1. BOUNDARY-VALUE PROBLEMS FOR LINEAR ELLIPTIC EQUATION OF 2ND ORDER [J].
BABUSKA, I ;
GUO, BQ .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1988, 19 (01) :172-203
[4]   REGULARITY OF THE SOLUTION OF ELLIPTIC PROBLEMS WITH PIECEWISE ANALYTIC DATA, .2. THE TRACE SPACES AND APPLICATION TO THE BOUNDARY-VALUE PROBLEMS WITH NONHOMOGENEOUS BOUNDARY-CONDITIONS [J].
BABUSKA, I ;
GUO, BQ .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (04) :763-781
[5]   THE P-VERSION AND H-P-VERSION OF THE FINITE-ELEMENT METHOD, AN OVERVIEW [J].
BABUSKA, I ;
SURI, M .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1990, 80 (1-3) :5-26
[6]  
BERNARDI C, PREPRINT
[7]  
Bernardi Christine., 1992, APPROXIMATIONS SPECT
[8]  
BOILLAT E, 1994, 2194 HELS U TECHN
[9]   STABILIZED MIXED METHODS FOR THE STOKES PROBLEM [J].
BREZZI, F ;
DOUGLAS, J .
NUMERISCHE MATHEMATIK, 1988, 53 (1-2) :225-235
[10]  
Brezzi F., 1991, SPRINGER SERIES COMP, V15
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