Mathematical analysis and numerical approximation of a general linearized poro-hyperelastic model

DOI10.1016/j.camwa.2020.07.025OpenAlexW3082027390MaRDI QIDQ2027627

Paolo Zunino, Luca Dedè, Nicolás Barnafi, Alfio M. Quarteroni

Publication date: 27 May 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2020.07.025

zbMATH Keywords

finite element approximationporomechanicsinf-sup stability condition

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items

Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema, Robust A Posteriori Error Analysis for Rotation-Based Formulations of the Elasticity/Poroelasticity Coupling, Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials, Numerical modeling of the brain poromechanics by high-order discontinuous Galerkin methods, Editorial: Robust and reliable finite element methods in poromechanics, Scalable and robust dual-primal Newton-Krylov deluxe solvers for cardiac electrophysiology with biophysical ionic models, Robust approximation of generalized Biot-Brinkman problems

Uses Software

• ARPACK
• SciPy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• General coupling of porous flows and hyperelastic formulations -- from thermodynamics principles to energy balance and compatible time schemes
• Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction
• A poroelastic model valid in large strains with applications to perfusion in cardiac modeling
• Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
• A numerical solution of the Navier-Stokes equations using the finite element technique
• A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model
• A general approach for modeling interacting flow through porous media under finite deformations
• Trends in continuum mechanics of porous media.
• Numerical analysis for an energy-stable total discretization of a poromechanics model with inf-sup stability
• Error estimates for a mixed finite element approximation of the Stokes equations
• Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
• Analysis of Mixed Finite Element Methods for the Stokes Problem: A Unified Approach
• Numerical solution of saddle point problems
• Generalized Inf-Sup Conditions for Chebyshev Spectral Approximation of the Stokes Problem
• STABILITY OF HIGHER ORDER TRIANGULAR HOOD-TAYLOR METHODS FOR THE STATIONARY STOKES EQUATIONS
• Three-Dimensional Finite Element Methods for the Stokes Problem
• ARPACK Users' Guide
• Rayleigh–Ritz approximation of the inf-sup constant for the divergence
• Mixed Finite Element Methods and Applications
• The inf‐sup constant for the divergence on corner domains
• Computational mechanics of the heart.