Extension of the method of auxiliary mapping for three-dimensional elliptic boundary value problems (Q2709662)

This paper is concerned with the study of the approximation of three-dimensional elliptic problems which contain singularities caused by non-smooth domains like those which appear in problems with crack front. These singularities appear in the neighbourhoods of the vertex, of the edge and of the vertex-edge.NEWLINENEWLINENEWLINEThe authors extend to three-dimensional problems the method of auxiliary mapping which was previously introduced and analyzed by \textit{I. Babuska} and \textit{H.-S. Oh} [Numer. Methods Partial Differ. Equations 6, No. 4, 371-392 (1990; Zbl 0717.65084); Comput. Methods Appl. Mech. Eng. 97, No. 2, 211-231 (1992; Zbl 0762.65059); J. Comput. Phys. 212, No. 2, 193-212 (1995; Zbl 0833.73061)] for two-dimensional problems. Beyond a detailed analysis of the approximation, the paper includes the constructions of the blending-type elemental mappings and some numerical experiments which illustrate the effectiveness of the method.