Uniformly well-posed hybridized discontinuous Galerkin/hybrid mixed discretizations for Biot's consolidation model
DOI10.1016/j.cma.2021.113991OpenAlexW3112019407MaRDI QIDQ2237486
Johannes Kraus, Maria Lymbery, Philip L. Lederer, Joachim Schöberl
Publication date: 27 October 2021
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.08584
Biot's consolidation modelhybrid discontinuous Galerkin methodshybrid mixed methodsnorm-equivalent preconditionersparameter-robust LBB stabilitystrongly mass conserving high-order discretizations
Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Flows in porous media; filtration; seepage (76S05) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)
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Cites Work
- A nonconforming finite element method for the Biot's consolidation model in poroelasticity
- Numerical computations with \(H(\mathop{div})\)-finite elements for the Brinkman problem
- A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations
- 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
- A course in elasticity. Translated by F. A. Ficken, with the editorial assistance of D. A. Simons
- Improved accuracy in finite element analysis of Biot's consolidation problem
- NETGEN: An advancing front 2D/3D-mesh generator based on abstract rules
- Diffusion in poro-elastic media
- Parameter-robust stability of classical three-field formulation of Biot's consolidation model
- Robust iterative schemes for non-linear poromechanics
- The numerical solution of differential-algebraic systems by Runge-Kutta methods
- New stabilized discretizations for poroelasticity and the Stokes' equations
- Iterative solvers for Biot model under small and large deformations
- A moving finite element framework for fast infiltration in nonlinear poroelastic media
- A high-order HDG method for the Biot's consolidation model
- A posteriori error estimates for Biot system using enriched Galerkin for flow
- Three-field mixed finite element methods for nonlinear elasticity
- High order exactly divergence-free Hybrid Discontinuous Galerkin methods for unsteady incompressible flows
- Space-time finite element approximation of the Biot poroelasticity system with iterative coupling
- Enriched Galerkin methods for two-phase flow in porous media with capillary pressure
- Error-bounds for finite element method
- 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
- Stable Cell-Centered Finite Volume Discretization for Biot Equations
- Uniformly Stable Discontinuous Galerkin Discretization and Robust Iterative Solution Methods for the Brinkman Problem
- Locking-Free Finite Element Methods for Poroelasticity
- A coupling of nonconforming and mixed finite element methods for Biot's consolidation model
- H(div)-CONFORMING FINITE ELEMENTS FOR THE BRINKMAN PROBLEM
- Preconditioning discretizations of systems of partial differential equations
- Parameter-Robust Discretization and Preconditioning of Biot's Consolidation Model
- The existence and uniqueness theorem in Biot's consolidation theory
- Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
- Finite element methods for coupled thermoelasticity and coupled consolidation of clay
- Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models
- Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
- Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
- On stability and convergence of finite element approximations of Biot's consolidation problem
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Local Discontinuous Galerkin Methods for the Stokes System
- A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities
- Hybrid Discontinuous Galerkin Methods with Relaxed H(div)-Conformity for Incompressible Flows. Part I
- A Mixed Finite Element Method for Nearly Incompressible Multiple-Network Poroelasticity
- A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems
- A locally conservative LDG method for the incompressible Navier-Stokes equations
- Mixed Finite Element Methods and Applications
- Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes
- Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity
- Robust Block Preconditioners for Biot’s Model
- Parameter-Robust Convergence Analysis of Fixed-Stress Split Iterative Method for Multiple-Permeability Poroelasticity Systems
- A Mass Conserving Mixed Stress Formulation for Stokes Flow with Weakly Imposed Stress Symmetry
- Conservative discretizations and parameter‐robust preconditioners for Biot and multiple‐network flux‐based poroelasticity models
- Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II
- A mass conserving mixed stress formulation for the Stokes equations
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