Local discontinuous Galerkin method for diffusion equations with reduced stabilization

We extend the results on minimal stabilization of Burman and Stamm[J. Sci. Comp., 33 (2007), pp. 183-208] to the case of the local discontinuous Galerkin methods on mixed form. The penalization term on the faces is relaxed to act only on a part of the polynomial spectrum. Stability in the form of a discrete inf-sup condition is proved and optimal convergence follows. Some numerical examples using high order approximation spaces illustrate the theory.


Published in:
Commun. Comput. Phys., 5, 498-514
Year:
2009
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 Record created 2007-10-08, last modified 2018-03-17

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