Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
First-order system least squares for second-order partial differential equations: part I
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
On the interface boundary condition of Beavers, Joseph, and Saffman
SIAM Journal on Applied Mathematics
Asymptotic Analysis of the Laminar Viscous Flow Over a Porous Bed
SIAM Journal on Scientific Computing
Multilevel Boundary Functionals for Least-Squares Mixed Finite Element Methods
SIAM Journal on Numerical Analysis
Coupling Fluid Flow with Porous Media Flow
SIAM Journal on Numerical Analysis
Mathematical and numerical models for coupling surface and groundwater flows
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
A Residual-Based A Posteriori Error Estimator for the Stokes-Darcy Coupled Problem
SIAM Journal on Numerical Analysis
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The coupled problem with Stokes flow in one subdomain and a Darcy flow model in a second subdomain is studied in this paper. Both flow problems are treated as first-order systems, involving pseudostress and velocity in the Stokes case and using a flux-pressure formulation in the Darcy subdomain as process variables, respectively. The Beavers-Joseph-Saffman interface conditions are treated by an appropriate interface functional which is added to the least squares functional associated with the subdomain problems. A combination of $H(\mathrm{div})$-conforming Raviart-Thomas and standard $H^1$-conforming elements is used for the Stokes as well as for the Darcy subsystem. The homogeneous least squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates. It also establishes the fact that the local evaluation of the least squares functional itself constitutes an a posteriori error estimator to be used for adaptive refinement strategies.