ANISOTROPIC INTERPOLATION WITH APPLICATIONS TO THE FINITE-ELEMENT METHOD

被引：135

作者：

APEL, T ^{[1
]}

DOBROWOLSKI, M ^{[1
]}

机构：

[1] UNIV ERLANGEN NURNBERG,INST ANGEW MATH,W-8520 ERLANGEN,GERMANY

来源：

COMPUTING | 1992年 / 47卷 / 3-4期

关键词：

FINITE ELEMENT METHOD; MULTIVARIATE INTERPOLATION;

D O I：

10.1007/BF02320197

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The usual Bramble-Hilbert theory is extended for proving more refined estimates of the interpolation error. For a large class of finite elements, it is shown that one can derive benefit from the presence of small and even large angles of the elements. For bilinear shape functions on rectangular grids it is proved that interpolation and finite element approximation error coincide. As an example, we consider the finite element approximation for problems on domains containing edges.

引用

页码：277 / 293

页数：17

共 22 条

[1]

Adams RA., 2003, PURE APPL MATH SOB O, V2

[2]

APEL T, 1991, FINITE ELEMENTE METH

[3]

ARBENTZ P, 1982, IMA J NUMER ANAL, V29, P475

[4]

Arnold D., 1984, CALCOLO, V21, P337, DOI 10.1007/bf02576171

[5]

BARNHILL RE, 1981, IMA J NUMER ANAL, V28, P95

[6] BOUNDS FOR A CLASS OF LINEAR FUNCTIONALS WITH APPLICATIONS TO HERMITE INTERPOLATION [J].

BRAMBLE, JH ;

HILBERT, SR .

NUMERISCHE MATHEMATIK, 1971, 16 (04) :362-&

[7] ESTIMATION OF LINEAR FUNCTIONALS ON SOBOLEV SPACES WITH APPLICATION TO FOURIER TRANSFORMS AND SPLINE INTERPOLATION [J].

BRAMBLE, JH ;

HILBERT, SR .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1970, 7 (01) :112-&

[8]

Ciarlet P. G., 2002, FINITE ELEMENT METHO

[9] MULTIPOINT TAYLOR FORMULAS AND APPLICATIONS TO FINITE ELEMENT METHOD [J].

CIARLET, PG ;

WAGSCHAL, C .

NUMERISCHE MATHEMATIK, 1971, 17 (01) :84-&

[10]

Clement P., 1975, RAIRO ANAL NUMER R, V2, P77

← 1 2 3 →