ASYMPTOTIC ERROR EXPANSIONS FOR THE FINITE ELEMENT METHOD FOR SECOND ORDER ELLIPTIC PROBLEMS IN RN, N ≥ 2. I: LOCAL INTERIOR EXPANSIONS

被引：13

作者：

Asadzadeh, M. ^{[1
]}

Schatz, A. H. ^{[2
]}

Wendland, W. ^{[3
]}

机构：

[1] Chalmers Univ Technol, Dept Math, SE-41296 Gothenburg, Sweden

[2] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

[3] Univ Stuttgart, Inst Appl Anal & Numer Simulat, D-75069 Stuttgart, Germany

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2010年 / 48卷 / 05期

关键词：

local estimates; interior expansions; asymptotic error expansion inequalities; similarity of subspaces; scaling; finite element method; elliptic equations; RICHARDSON EXTRAPOLATION; IRREGULAR GRIDS; APPROXIMATION; SUPERCONVERGENCE; INEQUALITIES; DOMAINS;

D O I：

10.1137/080742737

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our aim here is to give sufficient conditions on the finite element spaces near a point so that the error in the finite element method for the function and its derivatives at the point have exact asymptotic expansions in terms of the mesh parameter h, valid for h sufficiently small. Such expansions are obtained from the so-called asymptotic expansion inequalities valid in RN for N >= 2, studies by Schatz in [Math. Comp., 67 (1998), pp. 877-899] and [SIAM J. Numer. Anal., 38 (2000), pp. 1269-1293].

引用

页码：2000 / 2017

页数：18

共 37 条

[31] Pointwise error estimates for differences in piecewise linear finite element approximations [J].

Schatz, AH ;

Wahlbin, LB .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2003, 41 (06) :2149-2160

[32] MAXIMUM NORM ESTIMATES IN THE FINITE-ELEMENT METHOD ON PLANE POLYGONAL DOMAINS .2. REFINEMENTS [J].

SCHATZ, AH ;

WAHLBIN, LB .

MATHEMATICS OF COMPUTATION, 1979, 33 (146) :465-492

[33] MAXIMUM NORM ESTIMATES IN FINITE-ELEMENT METHOD ON PLANE POLYGONAL DOMAINS .1. [J].

SCHATZ, AH ;

WAHLBIN, LB .

MATHEMATICS OF COMPUTATION, 1978, 32 (141) :73-109

[34] OPTIMAL LINFINITY ESTIMATES FOR FINITE-ELEMENT METHOD ON IRREGULAR MESHES [J].

SCOTT, R .

MATHEMATICS OF COMPUTATION, 1976, 30 (136) :681-697

[35] ASYMPTOTIC EXPANSIONS AND L-INFINITY-ERROR ESTIMATES FOR MIXED FINITE-ELEMENT METHODS FOR 2ND ORDER ELLIPTIC PROBLEMS [J].

WANG, J .

NUMERISCHE MATHEMATIK, 1989, 55 (04) :401-430

[36]

XU J, 2004, MATH COMPUT, V73, P1153

[37]

丁彦恒, 1989, Systems Science and Mathematical Science, V2, P54

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