Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems

Authors:
Santiago Badia;Ramon Codina
Affiliations:
sbadia@cimne.upc.edu;ramon.codina@upc.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2009

Citing 0
Cited 6

Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction

Journal of Computational Physics
Approximation of the inductionless MHD problem using a stabilized finite element method

Journal of Computational Physics
Long-Term Stability Estimates and Existence of a Global Attractor in a Finite Element Approximation of the Navier-Stokes Equations with Numerical Subgrid Scale Modeling

SIAM Journal on Numerical Analysis
Stokes, Maxwell and Darcy: A single finite element approximation for three model problems

Applied Numerical Mathematics
Long time stability of four methods for splitting the evolutionary Stokes-Darcy problem into Stokes and Darcy subproblems

Journal of Computational and Applied Mathematics
A Nodal-based Finite Element Approximation of the Maxwell Problem Suitable for Singular Solutions

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper we propose stabilized finite element methods for both Stokes' and Darcy's problems that accommodate any interpolation of velocities and pressures. Apart from the interest of this fact, the important issue is that we are able to deal with both problems at the same time, in a completely unified manner, in spite of the fact that the functional setting is different. Concerning the stabilization formulation, we discuss the effect of the choice of the length scale appearing in the expression of the stabilization parameters, both in what refers to stability and to accuracy. This choice is shown to be crucial in the case of Darcy's problem. As an additional feature of this work, we treat two types of stabilized formulations, showing that they have a very similar behavior.