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