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

In this paper, we extend the method of auxiliary mapping (MAM), introduced by Babuska and Oh, to three dimensions so that the extended MAM (3-D MAM) c an effectively handle three-dimensional elliptic problems containing the si ngularities caused by the non-smooth domains. There are three type of singu larities caused by non-smoothness of domains in R-3: the vertex, the edge, and the vertex-edge combined singularities. To deal with the singularities of these types, we present three auxiliary mappings and formulas for the tr ansformed bilinear forms and the transformed linear functionals by these au xiliary mappings. Then we present 3-D MAM and constructions of the blending -type elemental mappings for elements containing singularities. Numerical e xperiments that show the effectiveness of 3-D MAM are provided. Copyright ( C) 2001 John Wiley & Sons, Ltd.