Displaying similar documents to “Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations”

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

Ludovic Moya (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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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...

Stabilized Galerkin methods for magnetic advection

Holger Heumann, Ralf Hiptmair (2013)

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

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Taking the cue from stabilized Galerkin methods for scalar advection problems, we adapt the technique to boundary value problems modeling the advection of magnetic fields. We provide rigorous error estimates for both fully discontinuous piecewise polynomial trial functions and -conforming finite elements.

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...