A Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equation
From MaRDI portal
Publication:1033502
DOI10.1016/j.cma.2007.01.004zbMath1173.76329OpenAlexW2123597308MaRDI QIDQ1033502
Leopoldo P. Franca, Frédéric Valentin, Gabriel R. Barrenechea
Publication date: 6 November 2009
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2007.01.004
Flows in porous media; filtration; seepage (76S05) Finite element methods applied to problems in fluid mechanics (76M10)
Related Items
Revisiting generalized FEM: a Petrov-Galerkin enrichment based FEM interpolation for Helmholtz problem, On finite element methods for heterogeneous elliptic problems, Unconditionally stable mixed finite element methods for Darcy flow, A family of Multiscale Hybrid-Mixed finite element methods for the Darcy equation with rough coefficients, Unnamed Item, A unified mixed finite element approximations of the Stokes-Darcy coupled problem, Meshless analysis of Darcy flow with a variational multiscale interpolating element-free Galerkin method, A residual local projection method for the Oseen equation, An adaptive stabilized finite element method for the Darcy's equations with pressure dependent viscosities, An adaptive multiscale hybrid-mixed method for the Oseen equations, A two-level enriched finite element method for a mixed problem, Stabilization arising from PGEM: A review and further developments, A Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equation, Beyond pressure stabilization: A low-order local projection method for the Oseen equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Finite element approximation of the Navier-Stokes equations
- 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
- A new finite element formulation for computational fluid dynamics. V: Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
- A new finite element formulation for computational fluid dynamics. VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces
- A posteriori error estimators for the Stokes equations
- A relationship between stabilized finite element methods and the Galerkin method with bubble functions
- Further considerations on residual-free bubbles for advective-diffusive equations
- On the stability of residual-free bubbles for convection-diffusion problems and their approximation by a two-level finite element method
- A multiscale finite element method for elliptic problems in composite materials and porous media
- \(b=\int g\)
- Mass lumping emanating from residual-free bubbles
- A priori and a posteriori analysis of finite volume discretizations of Darcy's equations
- On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation
- An unusual stabilized finite element method for a generalized Stokes problem
- A stabilized mixed finite element method for Darcy flow
- Residual-free bubbles for advection-diffusion problems: The general error analysis
- Higher-order gradient post-processings for second-order elliptic problems
- Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.)
- Error analysis of piecewise constant pressure approximations of Darcy's law
- A stabilized mixed discontinuous Galerkin method for Darcy flow
- A computational method for approximating a Darcy-Stokes system governing a vuggy porous medium
- A unified stabilized method for Stokes' and Darcy's equations
- A multiscale a posteriori error estimate
- Towards multiscale functions: enriching finite element spaces with local but not bubble-like functions
- Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem
- Global and Local Error Analysis for the Residual-Free Bubbles Method Applied to Advection-Dominated Problems
- A Posteriori Error Estimates Based on Hierarchical Bases
- A stabilized finite-element method for the Stokes problem including element and edge residuals
- Error Analysis of Galerkin Least Squares Methods for the Elasticity Equations
- Analysis of Locally Stabilized Mixed Finite Element Methods for the Stokes Problem
- A comparison of a posteriori error estimators for mixed finite element discretizations by Raviart-Thomas elements
- CHOOSING BUBBLES FOR ADVECTION-DIFFUSION PROBLEMS
- ConservativeP1 Conforming and Nonconforming Galerkin FEMs: Effective Flux Evaluation via a Nonmixed Method Approach
- Analysis of a Two-Scale, Locally Conservative Subgrid Upscaling for Elliptic Problems
- A Robust Finite Element Method for Darcy--Stokes Flow
- Optimal Selection of the Bubble Function in the Stabilization of the P1-P1 Element for the Stokes Problem
- A locally conservative least‐squares method for Darcy flows
- Stabilized Finite Element Methods Based on Multiscale Enrichment for the Stokes Problem
- Convergence Analysis of a Multiscale Finite Element Method for Singularly Perturbed Problems
- On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles
- A minimal stabilisation procedure for mixed finite element methods
