2018/07/03 by Mats K. Brun, Elyes Ahmed, Brun, Mats K. +5 · 2 citations
Computer Science · Engineering · #35Q79 (Secondary) #35Q86 (Primary) 35Q74 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.1807.01171
openalex publication_date 2018/07/03 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
This paper is concerned with the analysis of the quasi-static\nthermo-poroelastic model. This model is nonlinear and includes thermal effects\ncompared to the classical quasi-static poroelastic model (also known as Biot's\nmodel). It consists of a momentum balance equation, a mass balance equation,\nand an energy balance equation, fully coupled and nonlinear due to a convective\ntransport term in the energy balance equation. The aim of this article is to\ninvestigate, in the context of mixed formulations, the existence and uniqueness\nof a weak solution to this model problem. The primary variables in these\nformulations are the fluid pressure, temperature and elastic displacement as\nwell as the Darcy flux, heat flux and total stress. The well-posedness of a\nlinearized formulation is addressed first through the use of a Galerkin method\nand suitable a priori estimates. This is used next to study the well-posedness\nof an iterative solution procedure for the full nonlinear problem. A\nconvergence proof for this algorithm is then inferred by a contraction of\nsuccessive difference functions of the iterates using suitable norms.\n