Numerical approximation of distributed optimal control problems governed by linear thermo-poroelasticity
Abstract
In this paper, we propose and analyze a novel three-field symmetric formulation for optimal control problems governed by linear thermo-poroelasticity. The state variables are the solid displacement u, the fluid pressure p, and the temperature θ, and both the distributed fluid source mp and the distributed heat source mθ serve as control variables. We prove well-posedness of the symmetric differentiated formulation, establish the existence and uniqueness of an optimal control pair (m̅p,m̅θ), and derive the first-order necessary optimality conditions via a coupled three-field adjoint system. For the fully discrete scheme based on dG(0) time discretization, we employ a variational discretization approach for both controls and derive a priori error estimates of order 𝒪(hs + Δt) for the state, adjoint, and control errors. We also present manufactured-solution experiments that validate the fully discrete optimality system and illustrate the storage-degenerate regime covered by our analysis.
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BibTeX
@misc{lee2026numerical,
title = {{Numerical approximation of distributed optimal control problems governed by linear thermo-poroelasticity}},
author = {Jeonghun J. Lee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24448},
eprint = {2609.24448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24448},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Numerical approximation of distributed optimal control problems governed by linear thermo-poroelasticity
AU - Jeonghun J. Lee
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24448
UR - https://arxiv.org/abs/2609.24448
AB - In this paper, we propose and analyze a novel three-field symmetric formulation for optimal control problems governed by linear thermo-poroelasticity. The state variables are the solid displacement u, the fluid pressure p, and the temperature θ, and both the distributed fluid source m_p and the distributed heat source m_θ serve as control variables. We prove well-posedness of the symmetric differentiated formulation, establish the existence and uniqueness of an optimal control pair (m̅_p,m̅_θ), and derive the first-order necessary optimality conditions via a coupled three-field adjoint system. For the fully discrete scheme based on dG(0) time discretization, we employ a variational discretization approach for both controls and derive a priori error estimates of order 𝒪(h^s + Δt) for the state, adjoint, and control errors. We also present manufactured-solution experiments that validate the fully discrete optimality system and illustrate the storage-degenerate regime covered by our analysis.
ER -