Symmetric and non-symmetric discontinuous Galerkin methods stabilized using bubble enrichment

Comptes Rendus Mathematique

Volumn 346, Issue 1-2, 2008, Pages 103-106

  Burman, Erik ^a   Stamm, Benjamin ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38749120587     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2007.11.016     Document Type: Article

References (10)

1. Arnold D.N. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 4 (1982) 742-760
2. Arnold D.N., Brezzi F., Cockburn B., and Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 5 (2001/2002) 1749-1779 (electronic)
3. Baker G. Finite element methods for elliptic equations using nonconforming elements. Math. Comp. 31 (1977) 44-59
4. Brezzi F., and Marini L.D. Bubble stabilization of discontinuous Galerkin methods. In: Fitzgibbon W., Hoppe R., Periaux J., Pironneau O., and Vassilevski Y. (Eds). Advances in Numerical Mathematics, Proc. International Conference on the occasion of the 60th birthday of Y.A. Kuznetsov (2006), Institute of Numerical Mathematics of The Russian Academy of Sciences, Moscow 25-36
5. Burman E., Ern A., Mozolevski I., and Stamm B. The symmetric discontinuous Galerkin method does not need stabilization in 1d for polynomial orders p ≥ 2. C. R. Acad. Sci. Paris, Ser. I 345 10 (2007) 599-602
6. E. Burman, B. Stamm, Low order discontinuous Galerkin methods for second order elliptic problems, Technical Report 04-2007, EPFL-IACS, 2007
7. Larson M.G., and Niklasson A.J. Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case. Numer. Math. 99 (2004) 113-130
8. Larson M.G., and Niklasson A.J. Analysis of a nonsymmetric discontinuous Galerkin method for elliptic problems: stability and energy error estimates. SIAM J. Numer. Anal. 42 1 (2004) 252-264
9. Oden J.T., Babuška I., and Baumann C. A discontinuous hp finite element method for diffusion problems. J. Comput. Phys. 146 2 (1998) 491-519
10. Rivière B., Wheeler M.F., and Girault V. A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. SIAM J. Numer. Anal. 39 3 (2001) 902-931 (electronic)