A stabilizer-free weak Galerkin finite element method for an optimal control problem of a time fractional diffusion equation

Shuo Wang, Jie Ma and Ning Du

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 231, issue C, 99-118

Abstract: This paper proposes a fully discrete stabilizer-free weak Galerkin (SFWG) finite element approximation for an optimal control problem driven by a time fractional diffusion equation.We focus on the spatial discretization of the SFWG finite element approximation to establish a semi-discrete scheme,followed by the application of L1 discretization to the Caputo fractional derivative in time to derive a fully discrete scheme.We then prove a priori error estimate for the discrete schemes.To reduce the computational complexity,we incorporate the proper orthogonal decomposition (POD) technique on the state and adjoint state systems to obtain a fully discrete reduced-order stabilizer-free weak Galerkin (ROSFWG) finite element method.Finally,the validity of the theoretical analysis is confirmed through numerical experiments.

Keywords: Optimal control problem; Time fractional diffusion equation; Stabilizer-free weak Galerkin finite element method; Proper orthogonal decomposition; A priori error estimate; Numerical experiments (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:231:y:2025:i:c:p:99-118

DOI: 10.1016/j.matcom.2024.11.019

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