Iterative Process for Numerical Recovering the Lowest Order Space-Wise Coefficient in Parabolic Equations

Abstract

In this work we suggest an iterative process for coefficient inverse problem. A parabolic equation in a bounded area supplied with initial condition and monotonic nondecreasing on time Dirichlet condition on a boundary is considered. We state a problem to recover the lowest order coefficient that depends only on spatial variables under an additional information as the observation of a solution taken at the final point of time. For numerical recovering of the coefficient we build the iterative process, at each iteration we perform finite-element approximation in space and fully implicit two-level discretization in time. For capabilities of given iterative process we present computational test for a model problem.