Missing boundary data reconstruction for the heat equation

Abstract

This work is concerned with the boundary data completion problem related to the heat equation in the special case of an annular domain. We first reformulate this inverse problem into an interfacial equation involving Steklov‐Poincaré operator based on fictitious domain decomposition techniques. We present some theoretical results. For solving the problem under consideration, we suggest a new numerical point of view which helps to reduce the computational cost using the Schur complement algorithm. We perform then the convergence analysis of this new approach in the annular domain. Several numerical experiments are shown to illustrate the efficiency of the proposed method.