Error analysis and adaptivity in three-dimensional linear elasticity by the usual and hypersingular boundary contour method
Two related topics are addressed. The first part of the paper proves that, for a certain 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 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, has been recently proposed for boundary integral equations as a local error estimator for a boundary elements. The second part of the paper is concerned with a definition of analogous local error estimator for the boundary contour method, for three-dimensional linear elasticity. This error estimator is then used to derive an \(h\)-adaptive meshing procedure. Numerical results are presented to demonstrate adaptive meshing for selected example problems.
scientific article; zbMATH DE number 1547217