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arXiv · 2605.30839

Distributed optimal control problems governed by poroelasticity equations

Arbaz Khan·Jeonghun J. Lee·Harpal Singh
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Abstract

In this paper, we propose and analyze a novel two-field symmetric formulation with solid displacement and fluid pressure as main unknowns for the Biot's consolidation model in poroelasticity. Firstly, we prove the well-posedness of the new formulation and then show the existence and uniqueness of optimal control where the fluid sources in the model act as a control variable. We prove a priori error estimates for the fully discrete scheme with backward Euler time discretization and a variational approximation of the control variable. A numerical example is presented to validate the performance of the proposed novel scheme.

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Arbaz Khan, Jeonghun J. Lee, Harpal Singh. 2026-05-29. Distributed optimal control problems governed by poroelasticity equations. https://arxiv.org/abs/2605.30839

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