Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
On error estimates of projection methods for Navier-Stokes equations: first-order schemes
SIAM Journal on Numerical Analysis
Interior penalty preconditioners for mixed finite element approximations of elliptic problems
Mathematics of Computation
Preconditioning in H(div) and applications
Mathematics of Computation
Uniform preconditioners for the time dependent Stokes problem
Numerische Mathematik
SIAM Journal on Numerical Analysis
Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)
A unified stabilized method for Stokes' and Darcy's equations
Journal of Computational and Applied Mathematics
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
SIAM Journal on Numerical Analysis
Partitioned Time Stepping for a Parabolic Two Domain Problem
SIAM Journal on Numerical Analysis
A Finite Element Method Based on Weighted Interior Penalties for Heterogeneous Incompressible Flows
SIAM Journal on Numerical Analysis
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We consider a time dependent coupled Stokes/Darcy flow problem and study an approximation method based on a unified finite element scheme complemented with implicit time stepping. Our finite element formulation relies on a weighing strategy in which the physical and discretization parameters are taken into account to robustly enforce interface and boundary conditions by means of the Nitsche method. We study absolute stability and convergence of the scheme, and discuss the algebraic properties of the associated discrete problem. Finally, we present numerical experiments confirming the predicted convergence behavior and algebraic properties, and report an application to the computational analysis of blood flow and plasma filtration in arteries after the implantation of a vascular graft.