A splitting based method for the numerical identification of a nonlinear convection coefficient in elliptic equations

Abstract

In this paper, we study a new class of nonlinear free convection coefficient identification problems to nonlinear elliptic equations. By introducing a least square functional depending on two state solutions and the total variation regularization term, we reformulate the addressed inverse problem into a constrained optimization problem. The existence of an optimal solution of the involved optimization problem is demonstrated. A meshless technique based on radial basis functions is employed as a discretization scheme. To handle the L1 norm of the total variation regularization functional, we employ the Alternating Direction Method of Multipliers to facilitate the minimization process. The convergence analysis of discrete optimization problem is established. At the end, several numerical examples are conducted to show the validity of the proposed numerical scheme.