Displaying similar documents to “Convergence of Finite Element Galerkin Approximations on Galerkin Problems”

Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods

Thirupathi Gudi, Johnny Guzmán (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large enough to stabilize the method. A central idea in the analysis is to construct an auxiliary solution from the discontinuous Galerkin solution by a simple post processing. Based on the auxiliary solution, we define the adaptive algorithm...

Stabilizations of the Baumann-Oden DG Formulation: the 3D Case

Paola F. Antonietti, Franco Brezzi, L.Donatella Marini (2008)

Bollettino dell'Unione Matematica Italiana

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We consider the Baumann-Oden Discontinuous Galerkin formulation in three dimensions in a rather general geometrical setting. Using only piecewise linear approximations (and no jump stabilizations) the method is clearly unstable. We discuss the relations of possible jump stabilizations and bubble stabilizations.

Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations

Ludovic Moya (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper we study the temporal convergence of a locally implicit discontinuous Galerkin method for the time-domain Maxwell’s equations modeling electromagnetic waves propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not clear due to the component splitting which can introduce order...