Distributed optimal control problems governed by poroelasticity equations
This work addresses the problem of optimal control in poroelasticity for engineers and researchers working with porous media, offering an incremental improvement in formulation and analysis.
This paper proposes a two-field symmetric formulation for Biot's consolidation model in poroelasticity, proving its well-posedness and the existence and uniqueness of optimal control. It also establishes a priori error estimates for a fully discrete scheme using backward Euler time discretization and variational approximation of the control variable.
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.