Local discontinuous Galerkin methods for the Stokes system
Bernardo Cockburn,
Guido Kanschat, Dominik Schötzau, Christoph Schwab
Abstract
In this paper, we introduce and analyze local discontinuous Galerkin
methods for the Stokes system. For arbitrary meshes with hanging
nodes and elements of various shapes 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>1. 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.