Jens Markus Melenk

Publication Activity (10 Years)

Years Active: 1999-2024
Publications (10 Years): 61

Top Topics

Boundary Conditions

Piecewise Polynomial

Top Venues

Comput. Math. Appl.

Numerische Mathematik

Publications

Chupeng Ma, Jens Markus Melenk
Exponential Convergence of a Generalized FEM for Heterogeneous Reaction-Diffusion Equations. Multiscale Model. Simul. 22 (1) (2024)
Maximilian Bernkopf, Jens Markus Melenk
Optimal convergence rates in L2 for a first order system least squares finite element method - part II: Inhomogeneous Robin boundary conditions. Comput. Math. Appl. 173 (2024)
Björn Bahr, Markus Faustmann, Jens Markus Melenk
An implementation of hp-FEM for the fractional Laplacian. CoRR (2024)
Leszek F. Demkowicz, Jens Markus Melenk, Jacob C. Badger, Stefan Henneking
Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides. Adv. Comput. Math. 50 (3) (2024)
Anton Arnold, Christian Klein, Jannis Körner, Jens Markus Melenk
Optimally truncated WKB approximation for the 1D stationary Schrödinger equation in the highly oscillatory regime. CoRR (2024)
Maximilian Bernkopf, Jens Markus Melenk
for a first order system least squares finite element method - Part II: inhomogeneous Robin boundary conditions. CoRR (2024)
Jens Markus Melenk, Ilaria Perugia, Alexander Rieder
FEM-BEM coupling for the high-frequency Helmholtz problem. CoRR (2024)
Michael Karkulik, Jens Markus Melenk, Alexander Rieder
On interpolation spaces of piecewise polynomials on mixed meshes. CoRR (2023)
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
Exponential Convergence of \(hp\)-FEM for the Integral Fractional Laplacian in Polygons. SIAM J. Numer. Anal. 61 (6) (2023)
Lehel Banjai, Jens Markus Melenk, Christoph Schwab
Exponential convergence of hp FEM for spectral fractional diffusion in polygons. Numerische Mathematik 153 (1) (2023)
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
Weighted analytic regularity for the integral fractional Laplacian in polyhedra. CoRR (2023)
Niklas Angleitner, Markus Faustmann, Jens Markus Melenk
Exponential meshes and H-matrices. Comput. Math. Appl. 130 (2023)
Niklas Angleitner, Markus Faustmann, Jens Markus Melenk
ℋ-inverses for RBF interpolation. Adv. Comput. Math. 49 (6) (2023)
Franz Achleitner, Goro Akagi, Christian Kuehn, Jens Markus Melenk, Jens D. M. Rademacher, Cinzia Soresina, Jichen Yang
Fractional Dissipative PDEs. CoRR (2023)
Jens Markus Melenk, Leszek F. Demkowicz, Stefan Henneking
Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides. CoRR (2023)
Jannis Körner, Anton Arnold, Christian Klein, Jens Markus Melenk
Optimally truncated WKB approximation for the highly oscillatory stationary 1D Schrödinger equation. CoRR (2023)
Maximilian Bernkopf, Théophile Chaumont-Frelet, Jens Markus Melenk
Wavenumber-explicit stability and convergence analysis of hp finite element discretizations of Helmholtz problems in piecewise smooth media. CoRR (2022)
Chupeng Ma, Jens Markus Melenk
Exponential convergence of a generalized FEM for heterogeneous reaction-diffusion equations. CoRR (2022)
Jens Markus Melenk, Alexander Rieder
An exponentially convergent discretization for space-time fractional parabolic equations using hp-FEM. CoRR (2022)
Markus Faustmann, Jens Markus Melenk, Maryam Parvizi
ℋ-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations. Adv. Comput. Math. 48 (5) (2022)
Alexander Rieder, Francisco-Javier Sayas, Jens Markus Melenk
Time domain boundary integral equations and convolution quadrature for scattering by composite media. Math. Comput. 91 (337) (2022)
Roland Becker, Maximilian Brunner, Michael Innerberger, Jens Markus Melenk, Dirk Praetorius
Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs. CoRR (2022)
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons. CoRR (2022)
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D. CoRR (2022)
Niklas Angleitner, Markus Faustmann, Jens Markus Melenk
Exponential meshes and H-matrices. CoRR (2022)
Roland Becker, Maximilian Brunner, Michael Innerberger, Jens Markus Melenk, Dirk Praetorius
Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs. Comput. Math. Appl. 118 (2022)
Markus Faustmann, Michael Karkulik, Jens Markus Melenk
Local Convergence of the FEM for the Integral Fractional Laplacian. SIAM J. Numer. Anal. 60 (3) (2022)
Jens Markus Melenk, Stefan A. Sauter
Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions. CoRR (2022)
Markus Faustmann, Jens Markus Melenk, Maryam Parvizi
Caccioppoli-type estimates and ℋ-matrix approximations to inverses for FEM-BEM couplings. Numerische Mathematik 150 (3) (2022)
Christoph Erath, Lorenzo Mascotto, Jens Markus Melenk, Ilaria Perugia, Alexander Rieder
Mortar Coupling of hp-Discontinuous Galerkin and Boundary Element Methods for the Helmholtz Equation. J. Sci. Comput. 92 (1) (2022)
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
Weighted analytic regularity for the integral fractional Laplacian in polygons. CoRR (2021)
Markus Faustmann, Jens Markus Melenk, Dirk Praetorius
Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. Math. Comput. 90 (330) (2021)
Markus Faustmann, Jens Markus Melenk, Maryam Parvizi
$\mathcal{H}$-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations. CoRR (2021)
Jens Markus Melenk, Stefan A. Sauter
Wavenumber-Explicit hp-FEM Analysis for Maxwell's Equations with Transparent Boundary Conditions. Found. Comput. Math. 21 (1) (2021)
Christoph Erath, Lorenzo Mascotto, Jens Markus Melenk, Ilaria Perugia, Alexander Rieder
Mortar coupling of hp-discontinuous Galerkin and boundary element methods for the Helmholtz equation. CoRR (2021)
Roland Becker, Maximilian Brunner, Michael Innerberger, Jens Markus Melenk, Dirk Praetorius
Goal-oriented adaptive finite element method for semilinear elliptic PDEs. CoRR (2021)
Jens Markus Melenk, Alexander Rieder
On superconvergence of Runge-Kutta convolution quadrature for the wave equation. Numerische Mathematik 147 (1) (2021)
Niklas Angleitner, Markus Faustmann, Jens Markus Melenk
H-inverses for RBF interpolation. CoRR (2021)
Franz Achleitner, Christian Kuehn, Jens Markus Melenk, Alexander Rieder
Metastable speeds in the fractional Allen-Cahn equation. Appl. Math. Comput. 408 (2021)
Niklas Angleitner, Markus Faustmann, Jens Markus Melenk
Approximating inverse FEM matrices on non-uniform meshes with $\mathcal{H}$-matrices. CoRR (2020)
Jens Markus Melenk, C. Rojik
On commuting p-version projection-based interpolation on tetrahedra. Math. Comput. 89 (321) (2020)
Lorenzo Mascotto, Jens Markus Melenk, Ilaria Perugia, Alexander Rieder
FEM-BEM mortar coupling for the Helmholtz problem in three dimensions. Comput. Math. Appl. 80 (11) (2020)
Markus Faustmann, Jens Markus Melenk, Maryam Parvizi
Caccioppoli-type estimates and H-Matrix approximations to inverses for FEM-BEM couplings. CoRR (2020)
Alexander Rieder, Francisco-Javier Sayas, Jens Markus Melenk
-semigroups in the graph norm with applications to time domain boundary integral equations. CoRR (2020)
Lehel Banjai, Jens Markus Melenk, Christoph Schwab
hp-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains. CoRR (2020)
Alexander Rieder, Francisco-Javier Sayas, Jens Markus Melenk
Time domain boundary integral equations and convolution quadrature for scattering by composite media. CoRR (2020)
Franz Achleitner, Christian Kuehn, Jens Markus Melenk, Alexander Rieder
Metastable Speeds in the Fractional Allen-Cahn Equation. CoRR (2020)
Markus Faustmann, Michael Karkulik, Jens Markus Melenk
Local convergence of the FEM for the integral fractional Laplacian. CoRR (2020)
Maximilian Bernkopf, Jens Markus Melenk
for a first order system least squares finite element method. Part I: homogeneous boundary conditions. CoRR (2020)
Jens Markus Melenk, Stefan A. Sauter, Céline Torres
Wavenumber Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems. SIAM J. Numer. Anal. 58 (4) (2020)
Lehel Banjai, Jens Markus Melenk, Christoph Schwab
Exponential Convergence of hp FEM for Spectral Fractional Diffusion in Polygons. CoRR (2020)
Lorenzo Mascotto, Jens Markus Melenk, Ilaria Perugia, Alexander Rieder
FEM-BEM mortar coupling for the Helmholtz problem in three dimensions. CoRR (2020)
Lehel Banjai, Jens Markus Melenk, Ricardo H. Nochetto, Enrique Otárola, Abner J. Salgado, Christoph Schwab
Tensor FEM for Spectral Fractional Diffusion. Found. Comput. Math. 19 (4) (2019)
Markus Faustmann, Jens Markus Melenk, Maryam Parvizi
On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion. CoRR (2019)
Michael Karkulik, Jens Markus Melenk
H-matrix approximability of inverses of discretizations of the fractional Laplacian. Adv. Comput. Math. 45 (5) (2019)
Markus Faustmann, Jens Markus Melenk
Local convergence of the boundary element method on polyhedral domains. Numerische Mathematik 140 (3) (2018)
Steffen Börm, Christina Börst, Jens Markus Melenk
An analysis of a butterfly algorithm. Comput. Math. Appl. 74 (9) (2017)
Markus Faustmann, Jens Markus Melenk
Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion problems: Corner domains. Comput. Math. Appl. 74 (7) (2017)
Markus Aurada, Michael Feischl, Thomas Führer, Michael Karkulik, Jens Markus Melenk, Dirk Praetorius
Local inverse estimates for non-local boundary integral operators. Math. Comput. 86 (308) (2017)
Steffen Börm, Jens Markus Melenk
Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis. Numerische Mathematik 137 (1) (2017)
Markus Faustmann, Jens Markus Melenk, Dirk Praetorius
Existence of ℋ-matrix approximants to the inverses of BEM matrices: The simple-layer operator. Math. Comput. 85 (297) (2016)
Markus Aurada, Jens Markus Melenk, Dirk Praetorius
FEM-BEM coupling for the large-body limit in micromagnetics. J. Comput. Appl. Math. 281 (2015)
Markus Faustmann, Jens Markus Melenk, Dirk Praetorius
ℋ-matrix approximability of the inverses of FEM matrices. Numerische Mathematik 131 (4) (2015)
Michael Karkulik, Jens Markus Melenk
Local high-order regularization and applications to hp-methods. Comput. Math. Appl. 70 (7) (2015)
Thomas Führer, Jens Markus Melenk, Dirk Praetorius, Alexander Rieder
Optimal additive Schwarz methods for the hp-BEM: The hypersingular integral operator in 3D on locally refined meshes. Comput. Math. Appl. 70 (7) (2015)
S. Esterhazy, Jens Markus Melenk
and in negative norms. Comput. Math. Appl. 67 (4) (2014)
Jens Markus Melenk, T. Wurzer
-projection on triangles and tetrahedra. Comput. Math. Appl. 67 (4) (2014)
Philipp Dörsek, Jens Markus Melenk
Symmetry-Free, p-Robust Equilibrated Error Indication for the hp-Version of the FEM in Nearly Incompressible Linear Elasticity. Comput. Methods Appl. Math. 13 (3) (2013)
Jens Markus Melenk, Asieh Parsania, Stefan A. Sauter
General DG-Methods for Highly Indefinite Helmholtz Problems. J. Sci. Comput. 57 (3) (2013)
Thomas Horger, Jens Markus Melenk, Barbara I. Wohlmuth
- and surface flux convergence in FEM. Comput. Vis. Sci. 16 (5) (2013)
Michael Feischl, Michael Karkulik, Jens Markus Melenk, Dirk Praetorius
Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method. SIAM J. Numer. Anal. 51 (2) (2013)
Jens Markus Melenk, Christos Xenophontos, Lisa Oberbroeckling
Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales. Adv. Comput. Math. 39 (2) (2013)
David P. Hewett, Stephen Langdon, Jens Markus Melenk
A High Frequency hp Boundary Element Method for Scattering by Convex Polygons. SIAM J. Numer. Anal. 51 (1) (2013)
Samuel Ferraz-Leite, Jens Markus Melenk, Dirk Praetorius
Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. Numerische Mathematik 122 (1) (2012)
Jens Markus Melenk, Barbara I. Wohlmuth
Quasi-Optimal Approximation of Surface Based Lagrange Multipliers in Finite Element Methods. SIAM J. Numer. Anal. 50 (4) (2012)
Jens Markus Melenk
Mapping Properties of Combined Field Helmholtz Boundary Integral Operators. SIAM J. Math. Anal. 44 (4) (2012)
Christos Xenophontos, Jens Markus Melenk, Niall Madden, Lisa Oberbroeckling, Pandelitsa Panaseti, Antri Zouvani
hp Finite Element Methods for Fourth Order Singularly Perturbed Boundary Value Problems. NAA (2012)
Lehel Banjai, Christian Lubich, Jens Markus Melenk
Runge-Kutta convolution quadrature for operators arising in wave propagation. Numerische Mathematik 119 (1) (2011)
Jens Markus Melenk, Stefan A. Sauter
Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation. SIAM J. Numer. Anal. 49 (3) (2011)
Maike Löhndorf, Jens Markus Melenk
Wavenumber-Explicit hp-BEM for High Frequency Scattering. SIAM J. Numer. Anal. 49 (6) (2011)
Jens Markus Melenk, Stefan A. Sauter
Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions. Math. Comput. 79 (272) (2010)
Jens Markus Melenk
On the convergence of Filon quadrature. J. Comput. Appl. Math. 234 (6) (2010)
Emmanuil H. Georgoulis, Edward J. C. Hall, Jens Markus Melenk
-Version Interior Penalty Discontinuous Galerkin Method. J. Sci. Comput. 42 (1) (2010)
Steffen Börm, Maike Löhndorf, Jens Markus Melenk
Approximation of Integral Operators by Variable-Order Interpolation. Numerische Mathematik 99 (4) (2005)
Jens Markus Melenk
hp-Interpolation of Nonsmooth Functions and an Application to hp-A posteriori Error Estimation. SIAM J. Numer. Anal. 43 (1) (2005)
Boris N. Khoromskij, Jens Markus Melenk
Boundary Concentrated Finite Element Methods. SIAM J. Numer. Anal. 41 (1) (2003)
Boris N. Khoromskij, Jens Markus Melenk
An Efficient Direct Solver for the Boundary Concentrated FEM in 2D. Computing 69 (2) (2002)
Tim Gutzmer, Jens Markus Melenk
Approximation orders for natural splines in arbitrary dimensions. Math. Comput. 70 (234) (2001)
Jens Markus Melenk, Barbara I. Wohlmuth
On residual-based a posteriori error estimation in hp-FEM. Adv. Comput. Math. 15 (1-4) (2001)
Jens Markus Melenk, N. P. Kirchner, Christoph Schwab
Spectral Galerkin Discretization for Hydrodynamic Stability Problems. Computing 65 (2) (2000)
Jens Markus Melenk
Operator adapted spectral element methods I: harmonic and generalized harmonic polynomials. Numerische Mathematik 84 (1) (1999)