543 research outputs found
A Polygonal Discontinuous Galerkin Method with Minus One Stabilization
We propose an Hybridized Discontinuous Galerkin method on polygonal
tessellations, stabilized by penalizing, locally in each element , a
residual term involving the fluxes, measured in the norm of the dual of
. The scalar product corresponding to such a norm is numerically
realized via the introduction of a (minimal) auxiliary space of VEM type.
Stability and optimal error estimates in the broken norm are proven under
a weak shape regularity assumption allowing the presence of very small edges.
The results of numerical tests confirm the theoretical estimates.Comment: 27 pages, 2 figure
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