40 citations · 75 across the 18 of their papers we have counts for
18 papers
Wavenumber-explicit -FEM analysis of Maxwell's equations with impedance boundary conditions in piecewise smooth media
Jens Markus Melenk, David Wörgötter
We consider the time-harmonic Maxwell equations with impedance boundary conditions on a bounded Lipschitz domain with analytic boundary . We suppose that consists of mul…
Wavenumber-explicit analytic regularity of the heterogeneous Maxwell equations with impedance boundary conditions
Jens Markus Melenk, David Wörgötter
We consider the time-harmonic Maxwell equations at a nonzero wavenumber on a bounded and simply connected Lipschitz domain with an analytic boundary , on wh…
Length-explicit stability analysis of Helmholtz problems in leaky circular waveguides
Leszek Demkowicz, Martin Halla, Jens Markus Melenk
Motivated by the study and simulation of long, coiled optical fibers we consider in this article a simplified model that is prevalent in the engineering community. Mathematically,…
Exponential Convergence of -FEM for the Integral Fractional Laplacian on cuboids
Björn Bahr, Markus Faustmann, Carlo Marcati +2
For the Dirichlet integral fractional Laplacian, we prove root exponential convergence of tensor-product -finite element approximations on , for forcing that is an…
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…
Fractional Dissipative PDEs
Franz Achleitner, Goro Akagi, Christian Kuehn +4
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we…
Optimally truncated WKB approximation for the highly oscillatory stationary 1D Schrödinger equation
Jannis Körner, Anton Arnold, Christian Klein +1
We discuss the numerical solution of initial value problems for in the highly oscillatory regime, i.e., with and . We an…
Robust exponential convergence of -FEM in balanced norms for singularly perturbed reaction-diffusion equations
Jens Markus Melenk, Christos Xenophontos
The -version of the finite element method is applied to a singularly perturbed reaction-diffusion equation posed in one- and two-dimensional domains with analytic boundary. On…
Simultaneous quasi-optimal convergence in FEM-BEM coupling
Jens Markus Melenk, Dirk Praetorius, Barbara Wohlmuth
We consider the symmetric FEM-BEM coupling that connects two linear elliptic second order partial differential equations posed in a bounded domain and its complement, where the…
Existence of -matrix approximants to the inverses of BEM matrices: the simple-layer operator
Markus Faustmann, Jens Markus Melenk, Dirk Praetorius
We consider the question of approximating the inverse of the Galerkin stiffness matrix obtained by discretizing the simple-layer operator $…