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189 people work at LJLL

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82 researchers and permanent lecturers

8 engineers, technicians and administrative staff

99 non-permanent staff

73 Phd students

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Figures : March 2019

2013-GdT ITER - A. Parsania

Séance du 20 Juin 2013.

ATTENTION EXCEPTIONNELLEMENT LA SEANCE AURA LIEU A 11H

Asieh Parsania

Institut für Mathematik

Universität Zürich

Title :

General DG-Methods for Highly Indefinite Helmholtz
Problems

Abstract :

We develop a stability and convergence theory for a Discontinuous Galerkin
formulation (DG) of a highly indefinite Helmholtz problem in $2d$ and $3d$. The theory
covers conforming as well as non-conforming generalized finite element methods. In
contrast
to conventional Galerkin methods where a minimal resolution condition is necessary
to guarantee the unique solvability,
it is proved that the DG-method admits a unique solution under
much weaker conditions. As an application we present the error analysis for the
$hp$-version
of the finite element method explicitly in terms of the mesh width $h$, polynomial
degree
$p$ and wavenumber $k$. It is shown that the optimal convergence order estimate is
obtained
under the conditions that $kh/ \sqrtp$ is sufficiently small and the polynomial
degree $p$ is at least
$O(log k)$. On regular meshes, the first condition is improved to the requirement
that $kh/p$ be
sufficiently small.