Analysis of a Discontinuous Finite Element Method for the Coupled Stokes and Darcy Problems
Journal of Scientific Computing
Analysis of a discontinuous finite element method for the coupled stokes and Darcy problems
Journal of Scientific Computing
A unified stabilized method for Stokes' and Darcy's equations
Journal of Computational and Applied Mathematics
On a MIC(0) preconditioning of non-conforming mixed FEM elliptic problems
Mathematics and Computers in Simulation
Boundary integral solutions of coupled Stokes and Darcy flows
Journal of Computational Physics
Weakly imposed Dirichlet boundary conditions for the Brinkman model of porous media flow
Applied Numerical Mathematics
Stokes-Darcy boundary integral solutions using preconditioners
Journal of Computational Physics
On the efficiency of symbolic computations combined with code generation for finite element methods
ACM Transactions on Mathematical Software (TOMS)
SyFi - an element matrix factory
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Efficient Assembly of $H(\mathrm{div})$ and $H(\mathrm{curl})$ Conforming Finite Elements
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
H(div) conforming finite element methods for the coupled Stokes and Darcy problem
Journal of Computational and Applied Mathematics
A Parallel Robin-Robin Domain Decomposition Method for the Stokes-Darcy System
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Preconditioning of linear systems arising in finite element discretizations of the brinkman equation
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Spectral methods based on new formulations for coupled Stokes and Darcy equations
Journal of Computational Physics
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Finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed. The system is approximately a linear Stokes problem when the perturbation parameter is large, while it degenerates to a mixed formulation of Poisson's equation as the perturbation parameter tends to zero. It is established, basically by numerical experiments, that most of the proposed finite element methods for Stokes problem or the mixed Poisson's system are not well behaved uniformly in the perturbation parameter. This is used as the motivation for introducing a new "robust" finite element which exhibits this property.