We analyze the singular behaviour of the Helmholtz equation set in a non-convex polygon. Classically, the solution of the problem is split into a regular part and one singular function for each re-entrant corner. The originality of our work is that the “amplitude” of the singular parts is bounded explicitly in terms of frequency. We show that for high frequency problems, the “dominant” part of the solution is the regular part. As an application, we derive sharp error estimates for finite element discretizations. These error estimates show that the “pollution effect” is not changed by the presence of singularities. Furthermore, a consequence of our theory is that locally refined meshes are not needed for high-frequency problems, unless a ver...
AbstractSome boundary value problems for a second-order elliptic partial differential equation in a ...
International audienceIn this work, we present a new solution representation for the Helmholtz trans...
Abstract. The paper is concerned with the finite element solution of the Poisson equation with ho-mo...
We analyze the singular behaviour of the Helmholtz equation set in a non-convex polygon. Classically...
In this paper we use an enriched approximation space for the efficient and accurate solution of the ...
In this study, a highly-accurate, conforming finite element method is developed and justified for th...
International audienceWe consider GMRES applied to discretisations of the high-frequency Helmholtz e...
The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary ...
We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a nontrapping...
Consider time-harmonic acoustic scattering problems governed by the Helmholtz equation in two and th...
The solution fields of Maxwell’s equations are known to exhibit singularities near corners, crack ti...
The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary ...
Elliptic boundary value problems for scalar operators or systems admit non-regular solu-tions when t...
International audienceFor the Helmholtz equation posed in the exterior of a Dirichlet obstacle, we p...
It is often noted that the Helmholtz equation is extremely difficult to solve, in particular, for hi...
AbstractSome boundary value problems for a second-order elliptic partial differential equation in a ...
International audienceIn this work, we present a new solution representation for the Helmholtz trans...
Abstract. The paper is concerned with the finite element solution of the Poisson equation with ho-mo...
We analyze the singular behaviour of the Helmholtz equation set in a non-convex polygon. Classically...
In this paper we use an enriched approximation space for the efficient and accurate solution of the ...
In this study, a highly-accurate, conforming finite element method is developed and justified for th...
International audienceWe consider GMRES applied to discretisations of the high-frequency Helmholtz e...
The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary ...
We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a nontrapping...
Consider time-harmonic acoustic scattering problems governed by the Helmholtz equation in two and th...
The solution fields of Maxwell’s equations are known to exhibit singularities near corners, crack ti...
The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary ...
Elliptic boundary value problems for scalar operators or systems admit non-regular solu-tions when t...
International audienceFor the Helmholtz equation posed in the exterior of a Dirichlet obstacle, we p...
It is often noted that the Helmholtz equation is extremely difficult to solve, in particular, for hi...
AbstractSome boundary value problems for a second-order elliptic partial differential equation in a ...
International audienceIn this work, we present a new solution representation for the Helmholtz trans...
Abstract. The paper is concerned with the finite element solution of the Poisson equation with ho-mo...