Local Discontinuous Galerkin Methods for the Stokes System

Authors:
Bernardo Cockburn;Guido Kanschat;Dominik Schötzau;Christoph Schwab
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2002

Citing 0
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Abstract

In this paper, we introduce and analyze local discontinuous Galerkin methods for the Stokes system. For a class of shape regular meshes with hanging nodes we derive a priori estimates for the L2-norm of the errors in the velocities and the pressure. We show that optimal-order estimates are obtained when polynomials of degree k are used for each component of the velocity and polynomials of degree k-1 for the pressure, for any $k\ge1$. We also consider the case in which all the unknowns are approximated with polynomials of degree k and show that, although the orders of convergence remain the same, the method is more efficient. Numerical experiments verifying these facts are displayed.