Operator adapted spectral element methods I: harmonic and generalized harmonic polynomials. - Jens Markus Melenk (Numerische Mathematik, 1999)

Spectral Galerkin Discretization for Hydrodynamic Stability Problems. - Jens Markus Melenk; N. P. Kirchner; Christoph Schwab (Computing, 2000)

On residual-based a posteriori error estimation in hp-FEM. - Jens Markus Melenk; Barbara I. Wohlmuth (Adv. Comput. Math., 2001)

Approximation orders for natural splines in arbitrary dimensions. - Tim Gutzmer; Jens Markus Melenk (Math. Comput., 2001)

An Efficient Direct Solver for the Boundary Concentrated FEM in 2D. - Boris N. Khoromskij; Jens Markus Melenk (Computing, 2002)

Boundary Concentrated Finite Element Methods. - Boris N. Khoromskij; Jens Markus Melenk (SIAM J. Numer. Anal., 2003)

Approximation of Integral Operators by Variable-Order Interpolation. - Steffen Börm; Maike Löhndorf; Jens Markus Melenk (Numerische Mathematik, 2005)

hp-Interpolation of Nonsmooth Functions and an Application to hp-A posteriori Error Estimation. - Jens Markus Melenk (SIAM J. Numer. Anal., 2005)

On the convergence of Filon quadrature. - Jens Markus Melenk (J. Comput. Appl. Math., 2010)

On the Suboptimality of the p-Version Interior Penalty Discontinuous Galerkin Method. - Emmanuil H. Georgoulis; Edward J. C. Hall; Jens Markus Melenk (J. Sci. Comput., 2010)

Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions. - Jens Markus Melenk; Stefan A. Sauter (Math. Comput., 2010)

Runge-Kutta convolution quadrature for operators arising in wave propagation. - Lehel Banjai; Christian Lubich; Jens Markus Melenk (Numerische Mathematik, 2011)

Wavenumber-Explicit hp-BEM for High Frequency Scattering. - Maike Löhndorf; Jens Markus Melenk (SIAM J. Numer. Anal., 2011)

Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation. - Jens Markus Melenk; Stefan A. Sauter (SIAM J. Numer. Anal., 2011)

hp Finite Element Methods for Fourth Order Singularly Perturbed Boundary Value Problems. - Christos Xenophontos; Jens Markus Melenk; Niall Madden; Lisa Oberbroeckling; Pandelitsa Panaseti; Antri Zouvani (NAA, 2012)

Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. - Samuel Ferraz-Leite; Jens Markus Melenk; Dirk Praetorius (Numerische Mathematik, 2012)

Mapping Properties of Combined Field Helmholtz Boundary Integral Operators. - Jens Markus Melenk (SIAM J. Math. Anal., 2012)

Quasi-Optimal Approximation of Surface Based Lagrange Multipliers in Finite Element Methods. - Jens Markus Melenk; Barbara I. Wohlmuth (SIAM J. Numer. Anal., 2012)

Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales. - Jens Markus Melenk; Christos Xenophontos; Lisa Oberbroeckling (Adv. Comput. Math., 2013)

Symmetry-Free, p-Robust Equilibrated Error Indication for the hp-Version of the FEM in Nearly Incompressible Linear Elasticity. - Philipp Dörsek; Jens Markus Melenk (Comput. Methods Appl. Math., 2013)

On optimal L2 - and surface flux convergence in FEM. - Thomas Horger; Jens Markus Melenk; Barbara I. Wohlmuth (Comput. Vis. Sci., 2013)

General DG-Methods for Highly Indefinite Helmholtz Problems. - Jens Markus Melenk; Asieh Parsania; Stefan A. Sauter (J. Sci. Comput., 2013)

Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method. - Michael Feischl; Michael Karkulik; Jens Markus Melenk; Dirk Praetorius (SIAM J. Numer. Anal., 2013)

A High Frequency hp Boundary Element Method for Scattering by Convex Polygons. - David P. Hewett; Stephen Langdon; Jens Markus Melenk (SIAM J. Numer. Anal., 2013)

An analysis of discretizations of the Helmholtz equation in L2 and in negative norms. - S. Esterhazy; Jens Markus Melenk (Comput. Math. Appl., 2014)

On the stability of the boundary trace of the polynomial L2-projection on triangles and tetrahedra. - Jens Markus Melenk; T. Wurzer (Comput. Math. Appl., 2014)

Optimal additive Schwarz methods for the hp-BEM: The hypersingular integral operator in 3D on locally refined meshes. - Thomas Führer; Jens Markus Melenk; Dirk Praetorius; Alexander Rieder (Comput. Math. Appl., 2015)

Local high-order regularization and applications to hp-methods. - Michael Karkulik; Jens Markus Melenk (Comput. Math. Appl., 2015)

FEM-BEM coupling for the large-body limit in micromagnetics. - Markus Aurada; Jens Markus Melenk; Dirk Praetorius (J. Comput. Appl. Math., 2015)

ℋ-matrix approximability of the inverses of FEM matrices. - Markus Faustmann; Jens Markus Melenk; Dirk Praetorius (Numerische Mathematik, 2015)

Existence of ℋ-matrix approximants to the inverses of BEM matrices: The simple-layer operator. - Markus Faustmann; Jens Markus Melenk; Dirk Praetorius (Math. Comput., 2016)

An analysis of a butterfly algorithm. - Steffen Börm; Christina Börst; Jens Markus Melenk (Comput. Math. Appl., 2017)

Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion problems: Corner domains. - Markus Faustmann; Jens Markus Melenk (Comput. Math. Appl., 2017)

Local inverse estimates for non-local boundary integral operators. - Markus Aurada; Michael Feischl; Thomas Führer; Michael Karkulik; Jens Markus Melenk; Dirk Praetorius (Math. Comput., 2017)

Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis. - Steffen Börm; Jens Markus Melenk (Numerische Mathematik, 2017)

Local convergence of the boundary element method on polyhedral domains. - Markus Faustmann; Jens Markus Melenk (Numerische Mathematik, 2018)

H-matrix approximability of inverses of discretizations of the fractional Laplacian. - Michael Karkulik; Jens Markus Melenk (Adv. Comput. Math., 2019)

On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion. - Markus Faustmann; Jens Markus Melenk; Maryam Parvizi (CoRR, 2019)

Tensor FEM for Spectral Fractional Diffusion. - Lehel Banjai; Jens Markus Melenk; Ricardo H. Nochetto; Enrique Otárola; Abner J. Salgado; Christoph Schwab (Found. Comput. Math., 2019)

FEM-BEM mortar coupling for the Helmholtz problem in three dimensions. - Lorenzo Mascotto; Jens Markus Melenk; Ilaria Perugia; Alexander Rieder (Comput. Math. Appl., 2020)

Runge-Kutta approximation for C0-semigroups in the graph norm with applications to time domain boundary integral equations. - Alexander Rieder; Francisco-Javier Sayas; Jens Markus Melenk (CoRR, 2020)

hp-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains. - Lehel Banjai; Jens Markus Melenk; Christoph Schwab (CoRR, 2020)

Approximating inverse FEM matrices on non-uniform meshes with $ mathcal{H}$-matrices. - Niklas Angleitner; Markus Faustmann; Jens Markus Melenk (CoRR, 2020)

Optimal convergence rates in L2 for a first order system least squares finite element method. Part I: homogeneous boundary conditions. - Maximilian Bernkopf; Jens Markus Melenk (CoRR, 2020)

On commuting p-version projection-based interpolation on tetrahedra. - Jens Markus Melenk; C. Rojik (Math. Comput., 2020)

Wavenumber Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems. - Jens Markus Melenk; Stefan A. Sauter; Céline Torres (SIAM J. Numer. Anal., 2020)

Metastable speeds in the fractional Allen-Cahn equation. - Franz Achleitner; Christian Kuehn 001; Jens Markus Melenk; Alexander Rieder (Appl. Math. Comput., 2021)

$ mathcal{H}$-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations. - Markus Faustmann; Jens Markus Melenk; Maryam Parvizi (CoRR, 2021)

Goal-oriented adaptive finite element method for semilinear elliptic PDEs. - Roland Becker; Maximilian Brunner; Michael Innerberger; Jens Markus Melenk; Dirk Praetorius (CoRR, 2021)

Weighted analytic regularity for the integral fractional Laplacian in polygons. - Markus Faustmann; Carlo Marcati; Jens Markus Melenk; Christoph Schwab (CoRR, 2021)

Wavenumber-Explicit hp-FEM Analysis for Maxwell's Equations with Transparent Boundary Conditions. - Jens Markus Melenk; Stefan A. Sauter (Found. Comput. Math., 2021)

Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. - Markus Faustmann; Jens Markus Melenk; Dirk Praetorius (Math. Comput., 2021)

On superconvergence of Runge-Kutta convolution quadrature for the wave equation. - Jens Markus Melenk; Alexander Rieder (Numerische Mathematik, 2021)

ℋ-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations. - Markus Faustmann; Jens Markus Melenk; Maryam Parvizi (Adv. Comput. Math., 2022)

Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs. - Roland Becker; Maximilian Brunner; Michael Innerberger; Jens Markus Melenk; Dirk Praetorius (Comput. Math. Appl., 2022)

An exponentially convergent discretization for space-time fractional parabolic equations using hp-FEM. - Jens Markus Melenk; Alexander Rieder (CoRR, 2022)

Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D. - Markus Faustmann; Carlo Marcati; Jens Markus Melenk; Christoph Schwab (CoRR, 2022)

Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs. - Roland Becker; Maximilian Brunner; Michael Innerberger; Jens Markus Melenk; Dirk Praetorius (CoRR, 2022)

Mortar Coupling of hp-Discontinuous Galerkin and Boundary Element Methods for the Helmholtz Equation. - Christoph Erath; Lorenzo Mascotto; Jens Markus Melenk; Ilaria Perugia; Alexander Rieder (J. Sci. Comput., 2022)

Time domain boundary integral equations and convolution quadrature for scattering by composite media. - Alexander Rieder; Francisco-Javier Sayas; Jens Markus Melenk (Math. Comput., 2022)

Caccioppoli-type estimates and ℋ-matrix approximations to inverses for FEM-BEM couplings. - Markus Faustmann; Jens Markus Melenk; Maryam Parvizi (Numerische Mathematik, 2022)

Local Convergence of the FEM for the Integral Fractional Laplacian. - Markus Faustmann; Michael Karkulik; Jens Markus Melenk (SIAM J. Numer. Anal., 2022)

Exponential meshes and H-matrices. - Niklas Angleitner; Markus Faustmann; Jens Markus Melenk (Comput. Math. Appl., 2023)

On interpolation spaces of piecewise polynomials on mixed meshes. - Michael Karkulik; Jens Markus Melenk; Alexander Rieder (CoRR, 2023)

Weighted analytic regularity for the integral fractional Laplacian in polyhedra. - Markus Faustmann; Carlo Marcati; Jens Markus Melenk; Christoph Schwab (CoRR, 2023)

Optimally truncated WKB approximation for the highly oscillatory stationary 1D Schrödinger equation. - Jannis Körner; Anton Arnold; Christian Klein 002; Jens Markus Melenk (CoRR, 2023)

Fractional Dissipative PDEs. - Franz Achleitner; Goro Akagi; Christian Kuehn 001; Jens Markus Melenk; Jens D. M. Rademacher; Cinzia Soresina; Jichen Yang (CoRR, 2023)

Exponential convergence of hp FEM for spectral fractional diffusion in polygons. - Lehel Banjai; Jens Markus Melenk; Christoph Schwab (Numerische Mathematik, 2023)

ℋ-inverses for RBF interpolation. - Niklas Angleitner; Markus Faustmann; Jens Markus Melenk (Adv. Comput. Math., 2023)

Exponential Convergence of (hp )-FEM for the Integral Fractional Laplacian in Polygons. - Markus Faustmann; Carlo Marcati; Jens Markus Melenk; Christoph Schwab (SIAM J. Numer. Anal., 2023)

An implementation of hp-FEM for the fractional Laplacian. - Björn Bahr; Markus Faustmann; Jens Markus Melenk (Comput. Math. Appl., 2024)

Optimal convergence rates in L2 for a first order system least squares finite element method - part II: Inhomogeneous Robin boundary conditions. - Maximilian Bernkopf; Jens Markus Melenk (Comput. Math. Appl., 2024)

FEM-BEM coupling for the high-frequency Helmholtz problem. - Jens Markus Melenk; Ilaria Perugia; Alexander Rieder (CoRR, 2024)

Optimal convergence rates in L2 for a first order system least squares finite element method - Part II: inhomogeneous Robin boundary conditions. - Maximilian Bernkopf; Jens Markus Melenk (CoRR, 2024)

The Green's function for an acoustic half-space problem with impedance boundary conditions Part I: Representation formula. - C. Lin; Jens Markus Melenk; Stefan A. Sauter (CoRR, 2024)

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; Jens Markus Melenk; S. Sauter (CoRR, 2024)

Regularity of vector fields with piecewise regular curl and divergence. - Jens Markus Melenk; David Wörgötter (CoRR, 2024)

Parsimonious convolution quadrature. - Jens Markus Melenk; Jörg Nick (CoRR, 2024)

Wavenumber-explicit stability and convergence analysis of ℎ𝑝 finite element discretizations of Helmholtz problems in piecewise smooth media. - Maximilian Bernkopf; Théophile Chaumont-Frelet; Jens Markus Melenk (Math. Comput., 2024)

Exponential Convergence of a Generalized FEM for Heterogeneous Reaction-Diffusion Equations. - Chupeng Ma; Jens Markus Melenk (Multiscale Model. Simul., 2024)

Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides. - Leszek F. Demkowicz; Jens Markus Melenk; Jacob C. Badger; Stefan Henneking (Adv. Comput. Math., 2024)

Wavenumber-Explicit hp-FEM Analysis for Maxwell's Equations with Impedance Boundary Conditions. - Jens Markus Melenk; Stefan A. Sauter (Found. Comput. Math., 2024)

Optimally truncated WKB approximation for the 1D stationary Schrödinger equation in the highly oscillatory regime. - Anton Arnold; Christian Klein 002; Jannis Körner; Jens Markus Melenk (J. Comput. Appl. Math., 2025)

Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides. - Jens Markus Melenk; Leszek F. Demkowicz; Stefan Henneking (SIAM J. Math. Anal., 2025)