The p-version of the boundary element method for a three-dimensional
crack problem
Alexei Bespalov and Norbert Heuer
J. Integral Equations Appl. 17 (3), 243-258, 2005.
We study the p-version of the boundary element method for a crack problem in
linear elasticity with Dirichlet boundary conditions. The unknown jump of the
traction has strong edge singularities and is approximated by solving an integral
equation of the first kind with weakly singular operator.
We prove a quasi-optimal a priori error estimate in the energy norm. For sufficiently
smooth given data this gives a convergence like c p-1+ε
with ε>0. Here, p denotes the polynomial degree of the piecewise
polynomial functions used to approximate the unknown.