Boundary data completion for a diffusion-reaction equation by minimizing the energy error functional and applying the conjugate gradient method

Abstract

. In this paper, a boundary data completion problem for a diffusionreaction partial differential equations (PDEs) was considered in a 2D domain. In a first step, the classical KMF (Kozlov, Maz’ya, Fomin) algorithm was used with spectral element method to find an approximate solution to that problem. In a second step, an alternative way was proposed by using conjugate gradient method where a symmetric positive definite operator was designed. Obtained results are illustrated by some numerical tests by using Matlab software.