97 citations · 734 across the 50 of their papers we have counts for
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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…