Eigenpair Computation for Two-Dimensional Heat Conduction Singularities

Abstract

Here we present a numerical procedure based on the p-version of the finite element method for computing efficiently and reliably approximations to the eigenpairs associated with two-dimensional heat conduction singular points. The proposed method, called the “modified Steklov method,” is general, that is, applicable to singularities associated with corners, nonisotropic multimaterial interfaces, and abrupt changes in boundary conditions. We introduce the method and demonstrate some of its main characteristics on several numerical examples.