@article{JEONG2025303,
title = {Optimal control for Darcy's equation in a heterogeneous porous media},
journal = {Applied Numerical Mathematics},
volume = {207},
pages = {303-322},
year = {2025},
issn = {0168-9274},
doi = {https://doi.org/10.1016/j.apnum.2024.08.027},
url = {https://www.sciencedirect.com/science/article/pii/S0168927424002319},
author = {SeongHee Jeong and Sanghyun Lee},
keywords = {Optimal control, Darcy's flow, Heterogeneity,  interior penalty},
abstract = {In this paper, we investigate optimal control problems in heterogeneous porous media. The optimal control problem is governed by the Darcy's flow equation; where the pressure is the state variable and the source/sink is the control variable. Then we introduce the reduced optimal control problem which contains only the state variable by replacing the control variable with a dependent quantity of the state variable based on the Darcy's equation. Here we employ C0 interior penalty finite element methods for the spatial discretization to solve the reduced optimal control problem resulting in a fourth-order variational inequality. We use P2 Lagrange finite elements for C0 interior penalty methods, which require fewer degrees of freedom than C1 finite element methods. We provide a priori error estimates and stability analyses by considering a heterogeneous permeability coefficient. Several numerical examples validate the given theories and illustrate the capabilities of the proposed algorithm.}
}

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