A fully-Galerkin method for the numerical solution of an inverse problem in a parabolic partial differential equation

Abstract

A fully-Galerkin approach to the coefficient recovery (parameter identification) problem for a linear parabolic partial differential equation is introduced. The forward problem is discretised with a sinc basis in the temporal domain and a finite element basis in the spatial domain. Tikhonov regularisation is applied to deal with the ill-posedness of the inverse problem. In the solution of the resulting nonlinear optimisation problem, advantage is taken of the diagonalisation solution procedure used for the discretised forward problem. An example with noisy data is included.