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Symmetric and non-symmetric discontinuous Galerkin methods stabilized using bubble enrichment
journal contribution
posted on 2023-06-07, 21:35 authored by Erik Burman, Benjamin StammIn this Note we prove that in two and three space dimensions, the symmetric and non-symmetric discontinuous Galerkin methods for second order elliptic problems are stable when using piecewise linear elements enriched with quadratic bubbles without any penalization of the interelement jumps. The method yields optimal convergence rates in both the broken energy norm and, in the symmetric case, the L2-norm. Moreover the method can be written in conservative form with fluxes independent of any stabilization parameter.
History
Publication status
- Published
Journal
Comptes Rendus MathématiqueISSN
1631-073XIssue
1-2Volume
346Page range
103-106Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes