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 first part of the art icle proves that, for a certain admissible class of problems in linear elas ticity, the hypersingular boundary contour method (HBCM) can be collocated at all boundary points on the surface of a three-dimensional (3-D) body, in cluding those on boundary contours, edges and corners, because the HBCM-sha pe-functions satisfy, a priori, all the smoothness requirements for colloca tion at these points. In contrast, the hypersingular boundary element metho d needs, in general, relaxation of some of these smoothness requirements fo r its shape functions, even for collocation at regular points that lie on t he boundaries of boundary elements. A hypersingular residual, obtained from the standard and hypersingular boun dary integral equations (HBIEs), has been recently proposed as a local erro r estimator for a boundary element, for the boundary integral equation. The second part in the present article is concerned with a definition of an an alogous local error estimator for the boundary contour method, for 3-D line ar elasticity. This error estimator is then used to drive an h-adaptive mes hing procedure. Numerical results are presented to demonstrate adaptive mes hing for selected example problems. (C) 2000 Elsevier Science Ltd. All righ ts reserved.