Paper Detail
Arbaz Khan, Jeonghun J. Lee, Harpal Singh
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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@article{khan2026distributed,
title = {Distributed optimal control problems governed by poroelasticity equations},
author = {Arbaz Khan and Jeonghun J. Lee and Harpal Singh},
year = {2026},
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 },
url = {https://arxiv.org/abs/2605.30839},
keywords = {math.OC, math.NA},
eprint = {2605.30839},
archiveprefix = {arXiv},
}
{}