The Finite Element Method for Semilinear Parabolic Equations with Discontinuous Coefficients

Abstract

In this paper we investigate the existence, uniqueness and regularity of the solution of semilinear parabolic equations with coefficients that are discontinuous across the interface, and some prior estimates are obtained.\u00a0A net shape of the finite elements around the singular points was designed in [7] to solve the linear elliptic\u00a0 problems, by means of that net, we prove that the approximate solution has the same convergence rate as that without singularity.