Open AccessError estimates of element-free Galerkin method for potential problems
Author(s) -
Rongjun Cheng,
Cheng Yu-Min
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.6037
Subject(s) - galerkin method , basis function , discontinuous galerkin method , finite element method , function (biology) , mathematics , penalty method , element (criminal law) , sobolev space , error analysis , approximation error , space (punctuation) , basis (linear algebra) , boundary element method , mathematical analysis , mathematical optimization , computer science , geometry , physics , evolutionary biology , biology , political science , law , thermodynamics , operating system
The error estimates for moving least-square approximation, which is the method for obtaining the shape function in element-free Galerkin method, are presented in Sobolev space Wk,p(Ω) for high dimensional problems. Then on the basis of element-free Galerkin method for potential problems, the error estimates for element-free Galerkin method for potential problems, in which the essential boundary conditions are enforced by penalty methods, are obtained. The error estimates we present in this paper have optimal order when the nodes and shape functions satisfy certain conditions. From the error analysis, it is shown that the error bound of the potential problem is directly related to the radii of the weight functions. Two numerical examples are also given to verify the conclusions in this paper.