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A unified stabilized method for Stokes’ and Darcy's equations

Erik Burman ; Peter Hansbo (Institutionen för tillämpad mekanik, Beräkningsteknik)
Journal of Computational and Applied Mathematics Vol. 198 (2007), 1, p. 35-51.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Stokes’ equation, Darcy's equation, Stabilized methods, Finite element, Interior penalty method, Nitsche's method, Domain decomposition, Inf–sup condition



Denna post skapades 2007-01-09.
CPL Pubid: 24784

 

Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Beräkningsteknik (2005-2006)

Ämnesområden

Numerisk analys
Strömningsmekanik

Chalmers infrastruktur