Numerical identification of the leading coefficient of a parabolic equation

Abstract

For a multidimensional parabolic equation, we study the problem of finding the leading coefficient, which is assumed to depend only on time, on the basis of additional information about the solution at an interior point of the computational domain. For the approximate solution of the nonlinear inverse problem, we construct linearized approximations in time with the use of ordinary finite-element approximations with respect to space. The numerical algorithm is based on a special decomposition of the approximate solution for which the transition to the next time level is carried out by solving two standard elliptic problems. The capabilities of the suggested numerical algorithm are illustrated by the results of numerical solution of a model inverse two-dimensional problem.