Error analysis of primal discontinuous Galerkin methods for a mixed formulation of the Biot equations

DOI10.1016/j.camwa.2016.12.030zbMath1368.65195OpenAlexW2572055818MaRDI QIDQ2013459

Travis Thompson, Jun Tan, Béatrice Rivière

Publication date: 18 August 2017

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2016.12.030

zbMATH Keywords

error estimateslockingdiscontinuous Galerkinporoelasticity

Mathematics Subject Classification ID

Biomechanics (92C10) Biomechanical solid mechanics (74L15) 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 (18)

VIRTUAL ELEMENT APPROXIMATIONS FOR TWO SPECIES MODEL OF THE ADVECTION-DIFFUSION-REACTION IN POROELASTIC MEDIA ⋮ Unfitted finite element method for fully coupled poroelasticity with stabilization ⋮ Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation ⋮ Discontinuous Galerkin Approximation of the Fully Coupled Thermo-poroelastic Problem ⋮ Analysis of an embedded-hybridizable discontinuous Galerkin method for Biot's consolidation model ⋮ Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity ⋮ A virtual element method for overcoming locking phenomena in Biot’s consolidation model ⋮ Numerical solution of the Biot/elasticity interface problem using virtual element methods ⋮ A sequential discontinuous Galerkin method for the coupling of flow and geomechanics ⋮ A high-order HDG method for the Biot's consolidation model ⋮ Finite element solvers for Biot's poroelasticity equations in porous media ⋮ A mixed discontinuous Galerkin method for the wave equation ⋮ A splitting-based finite element method for the Biot poroelasticity system ⋮ Adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of Biot's consolidation model ⋮ Virtual element methods for the three-field formulation of time-dependent linear poroelasticity ⋮ Error analysis of a conforming and locking-free four-field formulation for the stationary Biot’s model ⋮ Discontinuous Galerkin method for the nonlinear Biot's model ⋮ Discontinuous Galerkin method for the fully dynamic Biot's model

Cites Work

• Modeling of convection-dominated thermoporomechanics problems using incomplete interior penalty Galerkin method
• Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach
• A coupling of mixed and discontinuous Galerkin finite element methods for poroelasticity
• Introduction to modelling of transport phenomena in porous media
• Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method
• Diffusion in poro-elastic media
• Poroelasticity
• Estimation of penalty parameters for symmetric interior penalty Galerkin methods
• 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 Nonconforming High-Order Method for the Biot Problem on General Meshes
• Convergence analysis of a new mixed finite element method for Biot's consolidation model
• The existence and uniqueness theorem in Biot's consolidation theory
• Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
• Poincaré--Friedrichs Inequalities for Piecewise H¹ Functions
• A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems

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