Nonconforming discretizations of a poromechanical model on general meshes
type: Distribution
access URL: https://theses.hal.science/tel-00957292
format: HTML
issued: 2026-05-06T02:30:20.020933
modified: 2026-05-06T02:30:19.972095

Nonconforming discretizations of a poromechanical model on general meshes
type: Dataset
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticsdoctoralthesis
keyword: volumes-finis
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: problemes-de-point-selle
keyword: general-meshes
keyword: poroelasticity
keyword: finite-volumes
keyword: maillages-generaux
keyword: poroelasticite
keyword: nonconforming-methods
keyword: verrouillage-numerique
keyword: numerical-locking
keyword: saddle-point-problems
keyword: theses
keyword: methodes-non-conformes
landing page: https://theses.hal.science/tel-00957292
description: This manuscript focuses on the conception of nonconforming discretization methods for a poromechanical model. The aim of this work is to ease the coupling between the geomechanics and the multiphase compositional Darcy flow in porous media by discretizing mechanics and flow on the same mesh, typically nonconforming as it represents the lithology. Hence, the novelty hinges on a nonconforming treatment of mechanics on general meshes. In this work, we focus on a linear elasticity model. The nonconforming approximation of such a model is not straightforward owing to its lack of coercivity (meaning that a discrete Korn's inequality must hold on a discontinuous discrete space) and to the numerical locking phenomenon occurring as the material becomes incompressible. In a first part, we design an approximation space on general meshes, which can be viewed as an extension of the so-called Crouzeix-Raviart space. We study its approximation and conformity properties, and prove that this latter is well-adapted to the design of a primal, coercive, and locking-free discretization of the elasticity model on general meshes. The proposed method is less costly than its finite element equivalent (in terms of properties) P2. In a second part, we tackle the nonconforming approximation of a coupled poroelasticity model. We study the convergence of a family of numerical schemes whose space discretization relies on the Gradient schemes framework, to which belongs the method developed for mechanics. We prove the convergence of such approximations toward the minimal regularity solution of the continuous problem, and independently of the choice of physical parameters
identifier: NNT: 2013PEST1168
issued: 2026-05-06T02:30:19.990098
language: en
modified: 2026-05-06T02:30:19.990103

test_moissonnage_selune
type: Agent