An H¹-Galerkin mixed finite element method for identification of time dependent parameters in parabolic problems

Abstract

A direct method of identification of time dependent parameters in a linear parabolic boundary value problem with over-specified total internal energy involves the flux at the boundary, and an H1 mixed formulation seems to be more suitable than the standard methods for such class of nonlocal problems. Therefore, this paper develops and analyses an H1-Galerkin mixed finite element method. Optimal error estimates in both primary and flux variables are derived in semidiscrete case. Moreover, a priori error estimate for the parameters is established. Based on linearised backward Euler method, a completely discrete scheme is proposed and optimal error analysis is derived. The results of the numerical experiments show the efficacy of the proposed method and confirm our theoretical results.