Error analysis and adaptivity in three-dimensional linear elasticity by the usual and hypersingular boundary contour method

Two related topics are addressed in this article. The ®rst part of the article proves that, for a certain admissible class of problems in linear elasticity, the hypersingular boundary contour method (HBCM) can be collocated at all boundary points on the surface of a three-dimensional (3-D) body, including those on boundary contours, edges and corners, because the HBCM-shape-functions satisfy, a priori, all the smoothness requirements for collocation at these points. In contrast, the hypersingular boundary element method needs, in general, relaxation of some of these smoothness requirements for its shape functions, even for collocation at regular points that lie on the boundaries of boundary elements. A hypersingular residual, obtained from the standard and hypersingular boundary integral equations (HBIEs), has been recently proposed as a local error estimator for a boundary element, for the boundary integral equation. The second part in the present article is concerned with a de®nition of an analogous local error estimator for the boundary contour method, for 3-D linear elasticity. This error estimator is then used to drive an h-adaptive meshing procedure. Numerical results are presented to demonstrate adaptive meshing for selected example problems