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Lin, Z., Ma, S.F. and Lai, M. (2020) Meshless Method for Solving Delayed Partial Differential Equations of Segmented Continuous Type. Journal of Shanghai Normal University (Natural Science Edition), 49, 381-386.

has been cited by the following article:

• 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.