97 citations · 734 across the 50 of their papers we have counts for
51 papers
Weighted analytic regularity for the integral fractional Laplacian in polyhedra
Markus Faustmann, Carlo Marcati, Jens Markus Melenk +1
On polytopal domains in , we prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian with analytic right-hand s…
Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides
Jens Markus Melenk, Leszek Demkowicz, Stefan Henneking
In a time-harmonic setting, we show for heterogeneous acoustic and homogeneous electromagnetic wavesguides stability estimates with the stability constant depending linearly on the…
On interpolation spaces of piecewise polynomials on mixed meshes
Michael Karkulik, Jens Markus Melenk, Alexander Rieder
We consider fractional Sobolev spaces , , on 2D domains and -conforming discretizations by globally continuous piecewise polynomials on a mesh consisting of s…
Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs
Roland Becker, Maximilian Brunner, Michael Innerberger +2
We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite…
Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons
Markus Faustmann, Carlo Marcati, Jens Markus Melenk +1
We prove exponential convergence in the energy norm of finite element discretizations for the integral fractional diffusion operator of order subject to homogene…
Exponential convergence of a generalized FEM for heterogeneous reaction-diffusion equations
Chupeng Ma, Jens Markus Melenk
A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter , based on locally appro…
Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D
Markus Faustmann, Carlo Marcati, Jens Markus Melenk +1
We prove weighted analytic regularity for the solution of the integral fractional Poisson problem on bounded intervals with analytic right-hand side. Based on this regularity resul…
Exponential meshes and -matrices
Niklas Angleitner, Markus Faustmann, Jens Markus Melenk
In our previous works, we proved that the inverse of the stiffness matrix of an -version finite element method (FEM) applied to scalar second order elliptic boundary value probl…
An exponentially convergent discretization for space-time fractional parabolic equations using -FEM
Jens Markus Melenk, Alexander Rieder
We consider a space-time fractional parabolic problem. Combining a sinc-quadrature based method for discretizing the Riesz-Dunford integral with -FEM in space yields an exponen…
Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions
Jens M. Melenk, Stefan A. Sauter
The time-harmonic Maxwell equations at high wavenumber k in domains with an analytic boundary and impedance boundary conditions are considered. A wavenumber-explicit stability and…
Goal-oriented adaptive finite element method for semilinear elliptic PDEs
Roland Becker, Maximilian Brunner, Michael Innerberger +2
We formulate and analyze a goal-oriented adaptive finite element method (GOAFEM) for a semilinear elliptic PDE and a linear goal functional. The strategy involves the finite elemen…
Weighted analytic regularity for the integral fractional Laplacian in polygons
Markus Faustmann, Carlo Marcati, Jens Markus Melenk +1
We prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian in polygons with analytic right-hand side. We localize the problem…
-inverses for RBF interpolation
Niklas Angleitner, Markus Faustmann, Jens Markus Melenk
We consider the interpolation problem for a class of radial basis functions (RBFs) that includes the classical polyharmonic splines (PHS). We show that the inverse of the system ma…
Mortar coupling of -discontinuous Galerkin and boundary element methods for the Helmholtz equation
Christoph Erath, Lorenzo Mascotto, Jens Markus Melenk +2
We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in thre…
-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations
Markus Faustmann, Jens Markus Melenk, Maryam Parvizi
The inverse of the stiffness matrix of the time-harmonic Maxwell equation with perfectly conducting boundary conditions is approximated in the blockwise low-rank format of ${\mathc…
Exponential Convergence of FEM for Spectral Fractional Diffusion in Polygons
Lehel Banjai, Jens M. Melenk, Christoph Schwab
For the spectral fractional diffusion operator of order in bounded, curvilinear polygonal domains we prove exponential convergence of two classes of discreti…
Time domain boundary integral equations and convolution quadrature for scattering by composite media (extended preprint)
Alexander Rieder, Francisco-Javier Sayas, Jens Markus Melenk
We consider acoustic scattering in heterogeneous media with piecewise constant wave number. The discretization is carried out using a Galerkin boundary element method in space and…
Metastable Speeds in the Fractional Allen-Cahn Equation
Franz Achleitner, Christian Kuehn, Jens Markus Melenk +1
We study numerically the one-dimensional Allen-Cahn equation with the spectral fractional Laplacian on intervals with homogeneous Neumann boundary conditions. In parti…
Local convergence of the FEM for the integral fractional Laplacian
Markus Faustmann, Michael Karkulik, Jens Markus Melenk
We provide for first order discretizations of the integral fractional Laplacian sharp local error estimates on proper subdomains in both the local -norm and the localized ener…
FEM-BEM mortar coupling for the Helmholtz problem in three dimensions
Lorenzo Mascotto, Jens Markus Melenk, Ilaria Perugia +1
We present a FEM-BEM coupling strategy for time-harmonic acoustic scattering in media with variable sound speed. The coupling is realized with the aid of a mortar variable that is…
-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains
Lehel Banjai, Jens M. Melenk, Christoph Schwab
In bounded, polygonal domains with Lipschitz boundary consisting of a finite number of Jordan curves admitting analytic parametrizations, we ana…
Runge-Kutta approximation for -semigroups in the graph norm with applications to time domain boundary integral equations
Alexander Rieder, Francisco-Javier Sayas, Jens Markus Melenk
We consider the approximation to an abstract evolution problem with inhomogeneous side constraint using -stable Runge-Kutta methods. We derive a priori estimates in norms other…
On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
Markus Faustmann, Jens Markus Melenk, Maryam Parvizi
We provide an endpoint stability result for Scott-Zhang type operators in Besov spaces. For globally continuous piecewise polynomials these are bounded from into $B^{3/2}…
On superconvergence of Runge-Kutta convolution quadrature for the wave equation
Jens Markus Melenk, Alexander Rieder
The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral equation methods. Two temporal discre…