Weak Galerkin finite element method for Biot's consolidation problem

DOI10.1016/j.cam.2017.09.019zbMath1376.65128OpenAlexW2756478493MaRDI QIDQ1675969

Xiaoping Xie, Yumei Chen, Gang Chen

Publication date: 3 November 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2017.09.019

zbMATH Keywords

error estimatesfinite element methodnumerical experimentinitial boundary value problemweak Galerkin methodBiot's consolidation problem

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Initial-boundary value problems for second-order parabolic equations (35K20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items

Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model ⋮ A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm ⋮ The nonconforming locking-free virtual element method for the Biot's consolidation model in poroelasticity ⋮ Weak Galerkin finite element method for a class of time fractional generalized Burgers' equation ⋮ Unnamed Item ⋮ Weak Galerkin finite element method for linear poroelasticity problems ⋮ Multirate Time Iterative Scheme with Multiphysics Finite Element Method For a Nonlinear Poroelasticity ⋮ A new over-penalized weak Galerkin method. III: Convection-diffusion-reaction problems ⋮ A locking-free and mass conservative H(div) conforming DG method for the Biot's consolidation model ⋮ Combining finite element and analytical methods to contact problems of 3D structure on soft foundation ⋮ Robust Globally Divergence-Free Weak Galerkin Finite Element Methods for Natural Convection Problems ⋮ Convergence analysis of \(H(\operatorname{div})\)-conforming finite element methods for a nonlinear poroelasticity problem ⋮ A stabilized hybrid mixed finite element method for poroelasticity ⋮ Weak Galerkin method with implicit \(\theta \)-schemes for second-order parabolic problems ⋮ On the locking-free three-field virtual element methods for Biot’s consolidation model in poroelasticity ⋮ Free vibration of functionally graded sandwich shallow shells on Winkler and Pasternak foundations with general boundary restraints ⋮ An over-penalized weak Galerkin method for parabolic interface problems with time-dependent coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation
• A robust weak Galerkin finite element method for linear elasticity with strong symmetric stresses
• A nonconforming finite element method for the Biot's consolidation model in poroelasticity
• A robust WG finite element method for convection-diffusion-reaction equations
• Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach
• A weak Galerkin finite element method for the Maxwell equations
• A coupling of mixed and discontinuous Galerkin finite element methods for poroelasticity
• Improved accuracy in finite element analysis of Biot's consolidation problem
• An investigation of the stability of numerical solutions of Biot's equations of consolidation
• A weak Galerkin finite element method for second-order elliptic problems
• A posteriori error estimates of discontinuous Galerkin method for nonmonotone quasi-linear elliptic problems
• An auxiliary space multigrid preconditioner for the weak Galerkin method
• A two-level algorithm for the weak Galerkin discretization of diffusion problems
• An efficient numerical scheme for the biharmonic equation by weak Galerkin finite element methods on polygonal or polyhedral meshes
• 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 nonconforming and mixed finite element methods for Biot's consolidation model
• Weak Galerkin finite element methods for Parabolic equations
• Convergence analysis of a new mixed finite element method for Biot's consolidation model
• Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation
• An Interior Penalty Finite Element Method with Discontinuous Elements
• On stability and convergence of finite element approximations of Biot's consolidation problem
• Asymptotic Behavior of Semidiscrete Finite-Element Approximations of Biot’s Consolidation Problem
• Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations
• Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes
• Galerkin Finite Element Methods for Parabolic Problems
• A Least-Squares Mixed Finite Element Method for Biot's Consolidation Problem in Porous Media