5 papers
Optimal trace norms for Helmholtz problems
Benedikt GräÃle
The natural energy norm for Helmholtz problems is weighted with the wavenumber modulus and induces weighted norms on the trace spaces by minimal ext…
Dirichlet-to-Neumann operator for the Helmholtz problem with general wavenumbers on the -sphere
Benedikt GräÃle, Stefan A. Sauter
This paper considers the Helmholtz problem in the exterior of a ball with Dirichlet boundary conditions and radiation conditions imposed at infinity. The differential Helmholtz ope…
BEM for variable coefficient second-order problems
Benedikt GräÃle, Stefan A. Sauter
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operator…
Guaranteed inf-sup bounds and existence verification for semilinear elliptic problems via nonconforming finite elements
Benedikt GräÃle
A Newton--Kantorovich-type argument enables the a posteriori existence verification of a unique regular root near a computed approximation, purely from computable data. This framew…
Stable skeleton integral equations for general coefficient Helmholtz transmission problems
Benedikt GräÃle, Ralf Hiptmair, Stefan Sauter
A novel variational formulation of layer potentials and boundary integral operators generalizes their classical construction by Green's functions, which are not explicitly availabl…