ON THE ERROR ESTIMATION OF THE FINITE ELEMENT METHOD FOR THE BOUNDARY VALUE PROBLEMS WITH SINGULARITY IN THE LEBESGUE WEIGHTED SPACE

被引：21

作者：

Rukavishnikov, V. A. ^{[1
,2
]}

Rukavishnikova, H. I. ^{[1
]}

机构：

[1] Russian Acad Sci, Far Eastern Branch, Ctr Comp, Khabarovsk 680000, Russia

[2] Far Eastern State Transport Univ, Khabarovsk, Russia

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2013年 / 34卷 / 12期

关键词：

Finite element method; R-v-generalized solution; Strong singularity of solution; NU-GENERALIZED SOLUTION; MAXWELL EQUATIONS; NONCOORDINATED DEGENERATION; COORDINATED DEGENERATION; DIRICHLET PROBLEM; INITIAL DATA; INPUT DATA; CONVERGENCE; DOMAINS; FEM;

D O I：

10.1080/01630563.2013.809582

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A boundary value problem is said to possess a strong singularity if its solution u does not belong to the Sobolev space W-2(1)(H-1) or, in other words, the Dirichlet integral of the solution u diverges. This article analyzes the finite element method for the boundary value problems with coordinated and uncoordinated degeneration of input data and with strong singularity of the solution. The scheme of the finite element method is constructed on the basis of the definition of R-generalized solution to the problem, and the finite element space contains singular power functions. It is established that the considered method has second order convergence to the exact R generalized solution in the norm of the Lebesgue weighted space.

引用

页码：1328 / 1347

页数：20

共 21 条

[1] On the finite element method for elliptic problems with degenerate and singular coefficients [J].

Arroyo, Daniel ;

Bespalov, Alexei ;

Heuer, Norbert .

MATHEMATICS OF COMPUTATION, 2007, 76 (258) :509-537

[2] Numerical solution to the time-dependent Maxwell equations in two-dimensional singular domains:: The Singular Complement Method [J].

Assous, F ;

Ciarlet, P ;

Segré, J .

JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 161 (01) :218-249

[3]

AUBIN J., 1967, Ann. Scuola Norm. Sup. Pisa Cl. Sci., V21, P599

[4]

CIARLET P. G., 2002, Classics in Appl. Math., V40

[5] Exponential convergence of hp-FEM for Maxwell equations with weighted regularization in polygonal domains [J].

Costabel, M ;

Dauge, M ;

Schwab, C .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2005, 15 (04) :575-622

[6] Analysis of a modified Schrodinger operator in 2D: Regularity, index, and FEM [J].

Li, Hengguang ;

Nistor, Victor .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 224 (01) :320-338

[7] CRITERION FOR QUASI-OPTIMALNESS OF RITZ METHOD [J].

NITSCHE, J .

NUMERISCHE MATHEMATIK, 1968, 11 (04) :346-&

[8] Coercive estimate for a boundary value problem with noncoordinated degeneration of the data [J].

Rukavishnikov, V. A. ;

Kuznetsova, E. V. .

DIFFERENTIAL EQUATIONS, 2007, 43 (04) :550-560

[9] Weighted finite element method for an elasticity problem with singularity [J].

Rukavishnikov, V. A. ;

Nikolaev, S. G. .

DOKLADY MATHEMATICS, 2013, 88 (03) :705-709

[10] A finite element method scheme for boundary value problems with noncoordinated degeneration of input data [J].

Rukavishnikov V.A. ;

Kuznetsova E.V. .

Numerical Analysis and Applications, 2009, 2 (03) :250-259

← 1 2 3 →