TITLE:
The Interpolating Element-Free Galerkin Method for an Optimal Control Problem Governed by Fourth-Order Parabolic Partial Differential Equations
AUTHORS:
Xuyan Kang, Tongjun Sun
KEYWORDS:
Interpolating Element-Free Galerkin Method, Optimal Control Problem, Moving Least Squares Approximation, A Priori Error Estimates
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
17,
2025
ABSTRACT: 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.