On finite element methods for heterogeneous elliptic problems

DOI10.1016/j.ijsolstr.2008.08.005zbMath1168.74459OpenAlexW2024088229MaRDI QIDQ838554

Abimael Fernando Dourado Loula, Maicon R. Correa, Elson M. Toledo, João Nisan C. Guerreiro

Publication date: 26 August 2009

Published in: International Journal of Solids and Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ijsolstr.2008.08.005

zbMATH Keywords

heterogeneous mediainterface conditionsdiscontinuous Galerkindarcy flowGalerkin least squaresstabilized mixed methods

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Inhomogeneity in solid mechanics (74E05) Finite element methods applied to problems in solid mechanics (74S05) Flows in porous media; filtration; seepage (76S05)

Related Items

Higher-order gradient post-processings for second-order elliptic problems, Accelerated reactive transport simulations in heterogeneous porous media using Reaktoro and Firedrake, Hierarchical high order finite element spaces in \(H(\operatorname{div},\Omega)\times H^1(\Omega)\) for a stabilized mixed formulation of Darcy problem, Comparing mixed hybrid finite element method with standard FEM in swelling simulations involving extremely large deformations, A unified mixed formulation naturally coupling Stokes and Darcy flows, Improved accuracy in finite element analysis of Biot's consolidation problem, A partition of unity finite element method for nonlinear transient diffusion problems in heterogeneous materials, On the composite discontinuous Galerkin method for simulations of electric properties of semiconductor devices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mixed discontinuous Galerkin methods for Darcy flow
• A Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equation
• Two families of mixed finite elements for second order elliptic problems
• Mixed Petrov-Galerkin methods for the Timoshenko beam problem
• A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov-Galerkin finite element formulation
• A variational principle for the Laplace's operator with application in the torsion of composite rods
• A discontinuous \(hp\) finite element method for diffusion problems
• Discretisation and multigrid solution of elliptic equations with mixed derivative terms and strongly discontinuous coefficients
• Discontinuous finite element formulations applied to cracked elastic domains
• A stabilized mixed finite element method for Darcy flow
• Higher-order gradient post-processings for second-order elliptic problems
• New formulations and numerical analysis of discontinuous Galerkin methods
• Stabilization mechanisms in discontinuous Galerkin finite element methods
• A stabilized mixed discontinuous Galerkin method for Darcy flow
• A discontinuous finite element formulation for Helmholtz equation
• Error-bounds for finite element method
• Unconditionally stable mixed finite element methods for Darcy flow
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Mixed and Hybrid Finite Element Methods
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Optimal error estimates for the hp-version interior penalty discontinuous Galerkin finite element method
• Stabilized velocity post‐processings for Darcy flow in heterogeneous porous media