A Spectral Element Method for Solving Backward Parabolic Problems

Abstract

In this article, some existence and uniqueness theorems for a quasisolution of backward parabolic problems are given. A computational algorithm to find the quasisolution is also provided. In this algorithm, in order to approximate the quasisolution, spectral element method is used. Since the obtained system of linear equations is ill-conditioned, we apply the Levenberg–Marquardt regularization. Finally, some numerical examples are given to show the efficiency and accuracy of the introduced method.