A unified stabilized method for Stokes’ and Darcy's equations
Journal article, 2007

We use the lowest possible approximation order, piecewise linear, continuous velocities and piecewise constant pressures to compute solutions to Stokes equation and Darcy's equation, applying an edge stabilization term to avoid locking. We prove that the formulation satisfies the discrete inf-sup condition, we prove an optimal a priori error estimate for both problems. The formulation is then extended to the coupled case using a Nitsche-type weak formulation allowing for different meshes in the two subdomains. Finally, we present some numerical examples verifying the theoretical predictions and showing the flexibility of the coupled approach.

Inf–sup condition

Interior penalty method

Finite element

Stokes’ equation

Domain decomposition

Darcy's equation

Nitsche's method

Stabilized methods

Author

Erik Burman

Ecole Polytechnique Federale De Lausanne

Peter F G Hansbo

Computational Technology

Journal of Computational and Applied Mathematics

0377-0427 (ISSN)

Vol. 198 1 35-51

Subject Categories

Computational Mathematics

Fluid Mechanics and Acoustics

DOI

10.1016/j.cam.2005.11.022

More information

Latest update

5/3/2018 1