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The hp ‐version of the BEM with quasi‐uniform meshes for a three‐dimensional crack problem: The case of a smooth crack having smooth boundary curve
Author(s) -
Bespalov Alexei
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20311
Subject(s) - mathematics , mathematical analysis , biharmonic equation , gravitational singularity , boundary value problem , dirichlet problem , degree of a polynomial , norm (philosophy) , polygon mesh , traction (geology) , polynomial , geometry , law , geomorphology , geology , political science
The article considers a three‐dimensional crack problem in linear elasticity with Dirichlet boundary conditions. The crack in this model problem is assumed to be a smooth open surface with smooth boundary curve. The h p ‐version of the boundary element method with weakly singular operator is applied to approximate the unknown jump of the traction which is not L 2 ‐regular due to strong edge singularities. Assuming quasi‐uniform meshes and uniform distributions of polynomial degrees, we prove an a priori error estimate in the energy norm. The estimate gives an upper bound for the error in terms of the mesh size h and the polynomial degree p . It is optimal in h for any given data and quasi‐optimal in p for sufficiently smooth data. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008