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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 StammWe 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.
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Publication status
- Published
Journal
Journal of Scientific ComputingISSN
0885-7474External DOI
Issue
2Volume
33Page range
183 - 208Department affiliated with
- Mathematics Publications
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- No
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- Yes
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2012-02-06Usage metrics
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