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Minimal stabilization for discontinuous Galerkin finite element methods for hyperbolic problems.

journal contribution
posted on 2023-06-08, 10:02 authored by E Burman, B Stamm
We consider a discontinuous Galerkin finite element method for the advection-reaction equation in two space-dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained by a penalization of only the upper portion of the polynomial spectrum of the jump of the solution over element edges. We prove stability in the standard $h$-weighted graph norm and obtain optimal order error estimates with respect to mesh-size.

History

Publication status

  • Published

Journal

Journal of Scientific Computing

ISSN

0885-7474

Issue

2

Volume

33

Page range

183 - 208

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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