Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion

DOI10.1137/21m1449695arXiv2109.15006OpenAlexW3204657013MaRDI QIDQ6156609

Kent-André Mardal, Bryan Gomez-Vargas, Unnamed Author, Ricardo Ruiz-Baier

Publication date: 14 June 2023

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.15006

zbMATH Keywords

mixed finite elementsporoelasticityperturbed saddle-pointstress-altered diffusion

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Medical applications (general) (92C50) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Computational methods for problems pertaining to biology (92-08)

Related Items (1)

New twofold saddle-point formulations for Biot poroelasticity with porosity-dependent permeability

Cites Work

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• Automated solution of differential equations by the finite element method. The FEniCS book
• On the effects of microstress on macroscopic diffusion processes
• Elliptic partial differential equations of second order
• Weakly imposed symmetry and robust preconditioners for Biot's consolidation model
• Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach
• Bounds of Riesz transforms on \(L^p\) spaces for second order elliptic operators.
• Theory and practice of finite elements.
• Analysis and mixed-primal finite element discretisations for stress-assisted diffusion problems
• Adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of Biot's consolidation model
• Robust error analysis of coupled mixed methods for Biot's consolidation model
• A coupled multipoint stress-multipoint flux mixed finite element method for the Biot system of poroelasticity
• Domain decomposition and partitioning methods for mixed finite element discretizations of the Biot system of poroelasticity
• The Biot-Stokes coupling using total pressure: formulation, analysis and application to interfacial flow in the eye
• A pseudostress-based mixed-primal finite element method for stress-assisted diffusion problems in Banach spaces
• Formulation and analysis of fully-mixed methods for stress-assisted diffusion problems
• An arbitrary Lagrangian-Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory
• A priori and a posteriori error analyses of augmented twofold saddle point formulations for nonlinear elasticity problems
• Locking-Free Finite Element Methods for Poroelasticity
• A Simple Introduction to the Mixed Finite Element Method
• Convergence analysis of a new mixed finite element method for Biot's consolidation model
• Parameter-Robust Discretization and Preconditioning of Biot's Consolidation Model
• Mixed finite element methods for linear elasticity with weakly imposed symmetry
• Finite Element Methods for Navier-Stokes Equations
• PEERS: A new mixed finite element for plane elasticity
• Mixed and Hybrid Finite Element Methods
• Variational Techniques for Elliptic Partial Differential Equations
• On the numerical analysis of nonlinear twofold saddle point problems
• Mixed Finite Element Methods and Applications
• Mathematical modelling of blood–brain barrier failure and oedema
• A Study of Two Modes of Locking in Poroelasticity
• Robust Preconditioners for Perturbed Saddle-Point Problems and Conservative Discretizations of Biot's Equations Utilizing Total Pressure
• Parameter Robust Preconditioning by Congruence for Multiple-Network Poroelasticity
• A mixed elasticity formulation for fluid–poroelastic structure interaction
• Coupling Stokes Flow with Inhomogeneous Poroelasticity
• Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity
• Conservative discretizations and parameter‐robust preconditioners for Biot and multiple‐network flux‐based poroelasticity models
• Finite element quasi-interpolation and best approximation
• The Mathematical Theory of Finite Element Methods
• On thea priori anda posteriori error analysis of a two-fold saddle-point approach for nonlinear incompressible elasticity

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