Convergence analysis of \(H(\operatorname{div})\)-conforming finite element methods for a nonlinear poroelasticity problem

DOI10.1155/2020/9464389zbMath1459.65227OpenAlexW3087005460MaRDI QIDQ2004208

Zhifeng Weng, Yuping Zeng, Fen Liang

Publication date: 14 October 2020

Published in: Discrete Dynamics in Nature and Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2020/9464389

Mathematics Subject Classification ID

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)

Related Items (1)

Multirate Time Iterative Scheme with Multiphysics Finite Element Method For a Nonlinear Poroelasticity

Cites Work

• Unnamed Item
• A nonconforming finite element method for the Biot's consolidation model in poroelasticity
• Analysis and numerical approximations of equations of nonlinear poroelasticity
• A simple preconditioner for a discontinuous Galerkin method for the Stokes problem
• \(H\)(div) conforming finite element methods for the coupled Stokes and Darcy problem
• A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability
• Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach
• A strongly conservative finite element method for the coupling of Stokes and Darcy flow
• A coupling of mixed and discontinuous Galerkin finite element methods for poroelasticity
• Two families of mixed finite elements for second order elliptic problems
• Improved accuracy in finite element analysis of Biot's consolidation problem
• A strongly conservative hybrid DG/mixed FEM for the coupling of Stokes and Darcy flow
• Robust three-field finite element methods for Biot's consolidation model in poroelasticity
• Weak Galerkin finite element method for Biot's consolidation problem
• Weakly imposed symmetry and robust preconditioners for Biot's consolidation model
• Weak Galerkin method for the Biot's consolidation model
• On the use of divergence balanced \(\mathbf{H}(\operatorname{div})\)-\(L^2\) pair of approximation spaces for divergence-free and robust simulations of Stokes, coupled Stokes-Darcy and Brinkman problems
• Robust error analysis of coupled mixed methods for Biot's consolidation model
• A high-order HDG method for the Biot's consolidation model
• A coupling of weak Galerkin and mixed finite element methods for poroelasticity
• Analysis of a discontinuous Galerkin method for the Biot's consolidation problem
• Stability and monotonicity for some discretizations of the Biot's consolidation model
• A coupling of mixed and continuous Galerkin finite element methods for poroelasticity. I: The continuous in time case
• A coupling of mixed and continuous Galerkin finite element methods for poroelasticity. II: The discrete-in-time case
• A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations
• A Nonconforming High-Order Method for the Biot Problem on General Meshes
• Locking-Free Finite Element Methods for Poroelasticity
• A coupling of nonconforming and mixed finite element methods for Biot's consolidation model
• Convergence analysis of a new mixed finite element method for Biot's consolidation model
• H(div)-CONFORMING FINITE ELEMENTS FOR THE BRINKMAN PROBLEM
• Parameter-Robust Discretization and Preconditioning of Biot's Consolidation Model
• High Order Hierarchical Divergence-Free Constrained Transport H(div) Finite Element Method for Magnetic Induction Equation
• Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
• Robust Preconditioners for a New Stabilized Discretization of the Poroelastic Equations
• Quasilinear poroelasticity: Analysis and hybrid finite element approximation
• New Finite Element Methods in Computational Fluid Dynamics by H(div) Elements
• A Robust Numerical Method for Stokes Equations Based on Divergence-FreeH(div) Finite Element Methods
• On stability and convergence of finite element approximations of Biot's consolidation problem
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Analysis of a multiphysics finite element method for a poroelasticity model
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• Asymptotic Behavior of Semidiscrete Finite-Element Approximations of Biot’s Consolidation Problem
• Mixed Finite Element Methods and Applications
• A Study of Two Modes of Locking in Poroelasticity
• An H(div)-Conforming Finite Element Method for the Biot Consolidation Model
• A Modified Weak Galerkin Finite Element Method for the Poroelasticity Problems
• Conservative discretizations and parameter‐robust preconditioners for Biot and multiple‐network flux‐based poroelasticity models
• Steady flow in a deformable porous medium

This page was built for publication: Convergence analysis of \(H(\operatorname{div})\)-conforming finite element methods for a nonlinear poroelasticity problem