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discrete compactness

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system
Emmanuel Creusé, Serge Nicaise
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 40 / Issue 2 / March 2006

Published online by Cambridge University Press:

21 June 2006, pp. 413-430

Print publication:

March 2006
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In this paper we prove the discrete compactness property for a discontinuous Galerkin approximation of Maxwell's systemon quite general tetrahedral meshes. As a consequence, a discrete Friedrichs inequality is obtainedand the convergence of the discrete eigenvalues to the continuous ones is deducedusing the theory of collectively compact operators.Some numerical experiments confirm the theoretical predictions.