## Bubble stabilized discontinuous Galerkin method for parabolic and elliptic problems

In this paper we give an analysis of a bubble stabilized discontinuous Galerkin method (BSDG) for elliptic and parabolic problems. The method consists of stabilizing the numerical scheme by enriching the discontinuous ﬁnite element space elementwise by quadratic non-conforming bubbles. This approach leads to optimal convergence in the space and time discretization parameters. Moreover the divergence of the diﬀusive ﬂuxes converges in the $L^2$ -norm independently of the geometry of the domain.

Published in:
Numerische Mathematik, 116, 2, 213-241
Year:
2010
Keywords:
Note:
Please cite the original report as: EPFL/IACS report 06.2008
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