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

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 hp-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.