40 citations · 75 across the 18 of their papers we have counts for
9 papers · 1 filter
Parsimonious convolution quadrature
Jens M. Melenk, Jörg Nick
We present a method to rapidly approximate convolution quadrature (CQ) approximations, based on a piecewise polynomial interpolation of the Laplace domain operator, which we call t…
A note on the shift theorem for the Laplacian in polygonal domains (extended version)
Jens Markus Melenk, Claudio Rojik
We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. T…
The Green`s function for an acoustic, half-space impedance problem Part II: Analysis of the slowly varying and the plane wave component
C. Lin, J. M. Melenk, S. Sauter
We show that the acoustic Green`s function for a half-space impedance problem in arbitrary spatial dimension d can be written as a sum of two terms, each of which is the product of…
Optimal convergence rates in for a first order system least squares finite element method -- Part II: inhomogeneous Robin boundary conditions
Maximilian Bernkopf, Jens Markus Melenk
We consider divergence-based high order discretizations of an -based first order system least squares formulation of a second order elliptic equation with Robin boundary condi…
Regularity of vector fields with piecewise regular curl and divergence
Jens Markus Melenk, David Wörgötter
We consider a bounded Lipschitz domain with sufficiently smooth boundary and prove piecewise Sobolev regularity of vector fields that have piecewise regula…
An explicit factorization of the Green's function for an acoustic half-space problem with impedance boundary conditions into an oscillatory exponential and a slowly varying function
C. Lin, J. M. Melenk, S. Sauter
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of t…
An implementation of hp-FEM for the fractional Laplacian
Björn Bahr, Markus Faustmann, Jens Markus Melenk
We consider the discretization of the -integral Dirichlet fractional Laplacian by -finite elements. We present quadrature schemes to set up the stiffness matrix and load ve…
FEM-BEM coupling for the high-frequency Helmholtz problem
Jens Markus Melenk, Ilaria Perugia, Alexander Rieder
We present a wavenumber-explicit analysis of FEM-BEM coupling methods for time-harmonic Helmholtz problems proposed in arXiv:2004.03523 for conforming discretizations and in arXiv:…
Optimally truncated WKB approximation for the 1D stationary Schrödinger equation in the highly oscillatory regime
Anton Arnold, Christian Klein, Jannis Körner +1
This paper is dedicated to the efficient numerical computation of solutions to the 1D stationary Schrödinger equation in the highly oscillatory regime. We compute an approximate so…