Author(s)

Xuyan Kang, Tongjun Sun^*

School of Mathematics, Shandong University, Jinan, China.

In this paper, we investigate a meshless approximation, the interpolating element-free Galerkin method, for an optimal control problem governed by fourth-order parabolic partial differential equations. The state, co-state and control variables are spatially discretized by an improved moving least squares approximation that satisfies the interpolation property, and time is discretized by a backward-Euler method. We derive some a priori error estimates for both the control and state approximations. Numerical experiments are presented to verify the theoretical results.

Interpolating Element-Free Galerkin Method, Optimal Control Problem, Moving Least Squares Approximation, A Priori Error Estimates

Kang, X. and Sun, T. (2025) The Interpolating Element-Free Galerkin Method for an Optimal Control Problem Governed by Fourth-Order Parabolic Partial Differential Equations. Journal of Applied Mathematics and Physics, 13, 3871-3901. doi: 10.4236/jamp.2025.1311217.