Minimal stabilization of discontinuous Galerkin finite element methods for hyperbolic problems

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 graphnorm and obtain optimal order error estimates with respect to mesh-size.


Published in:
Journal of Scientific Computing, 33, 2, 183-208
Year:
2007
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 Record created 2007-07-07, last modified 2018-03-17

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