# Bienvenue - Laboratoire Jacques-Louis Lions

## Partenariats

|
Internships (10th and 11th grades high school students)
Job shadowing (Year 10, Year 11 students) See https://www.math.univ-paris-diderot.fr/diffusion/index

### Key figures

#### 189 people work at LJLL

##### 90 permanent staff

82 researchers and permanent lecturers

8 engineers, technicians and administrative staff

##### 99 non-permanent staff

73 Phd students

14 Post-doc and ATER

12 emeritus scholars and external collaborators

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.