A Galerkin FE method for elliptic optimal control problem governed by 2D space-fractional PDEs

TL;DR

This paper introduces a Galerkin finite element method for solving 2D elliptic optimal control problems governed by Riesz space-fractional PDEs, providing error estimates and numerical validation.

Contribution

It develops a novel Galerkin FE approach with variational discretization for 2D fractional PDE control problems, including error analysis and numerical tests.

Findings

Error estimates for control, state, and costate variables

Numerical results confirm the method's accuracy

Effective handling of 2D space-fractional PDEs

Abstract

In this paper, we propose a Galerkin finite element method for the elliptic optimal control problem governed by the Riesz space-fractional PDEs on 2D domains with control variable being discretized by variational discretization technique. The optimality condition is derived and priori error estimates of control, costate and state variables are successfully established. Numerical test is carried out to illustrate the accuracy performance of this approach.