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 Babu ska and Oh, to three dimensions so that the extended MAM (3-D MAM) can e ectively handle three-dimensional elliptic problems containing the singularities caused by the non-smooth domains. There are three type of singularities caused by non-smoothness of domains in R3: 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 transformed bilinear forms and the transformed linear functionals by these auxiliary mappings. Then we present 3-D MAM and constructions of the blending-type elemental mappings for elements containing singularities. Numerical experiments that show the e ectiveness of 3-D MAM are provided