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01-12-2020 | Issue 4/2020

Calcolo 4/2020

A discontinuous Galerkin recovery scheme with stabilization for diffusion problems

Journal:
Calcolo > Issue 4/2020
Authors:
Mauricio Osorio, Wilmar Imbachí
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Abstract

In this work, ideas previously introduced for a discontinuous Galerkin recovery method in one dimension, that involves a penalty stabilization term, are extended to an elliptic differential equation in several dimensions and different types of boundary conditions and meshes. Using standard arguments for other existing discontinuous Galerkin methods, we show results of existence and uniqueness of the solution. Also, optimal convergence rates are proved theoretically and confirmed numerically. Likewise, the numerical experiments allow us to analyze of the effect of the stabilization parameter.

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