A stabilized mixed discontinuous Galerkin method for Darcy flow
نویسندگان
چکیده
A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes twoand three-dimensional constant-flow ‘‘patch tests’’ for distorted element geometries. The key ingredient in the formulation is a volumetric, residual-based, stabilization term that does not involve any mesh-dependent parameters. 2005 Elsevier B.V. All rights reserved.
منابع مشابه
A stabilized mixed finite element method for Darcy flow
We develop new stabilized mixed finite element methods for Darcy flow. Stability and an a priori error estimate in the ‘‘stability norm’’ are established. A wide variety of convergent finite elements present themselves, unlike the classical Galerkin formulation which requires highly specialized elements. An interesting feature of the formulation is that there are no mesh-dependent parameters. N...
متن کاملStabilized Mixed Finite Element Method for Transient Darcy Flow
Darcy flow is a steady-state model for laminar flow of a fluid through a porous medium. The present work proposes an extended model of laminar Darcy flow by introducing dynamic pressure and velocity to the classical formulation. The solution of the proposed time-space model is attained by discretizing the problem with a stabilized mixed Galerkin method in space and a forward Euler method in tim...
متن کاملDarcyLite: A Matlab Toolbox for Darcy Flow Computation
DarcyLite is a Matlab toolbox for numerical simulations of flow and transport in 2-dim porous media. This paper focuses on the finite element (FE) methods and the corresponding code modules in DarcyLite for solving the Darcy equation. Specifically, four major types of finite element solvers, the continuous Galerkin (CG), the discontinuous Galerkin (DG), the weak Galerkin (WG), and the mixed fin...
متن کاملA Hybrid Discontinuous Galerkin Method for Darcy-Stokes Problems
We propose and analyze a hybrid discontinuous Galerkin method for the solution of incompressible flow problems, which allows to deal with pure Stokes, pure Darcy, and coupled Darcy-Stokes flow in a unified manner. The flexibility of the method is demonstrated in numerical examples.
متن کاملUN CO RR EC TE D PR O O F 1 A Hybrid Discontinuous Galerkin Method 2 for Darcy - Stokes Problems 3
We propose and analyze a hybrid discontinuous Galerkin method for the solution 10 of incompressible flow problems, which allows to deal with pure Stokes, pure Darcy, and 11 coupled Darcy-Stokes flow in a unified manner. The flexibility of the method is demonstrated 12 in numerical examples.
متن کامل