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ORCIDJens Markus Melenk
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- affiliation: TU Wien, Vienna, Austria
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2020 – today
- 2025
[j60]Anton Arnold
, Christian Klein, Jannis Körner, Jens Markus Melenk:
Optimally truncated WKB approximation for the 1D stationary Schrödinger equation in the highly oscillatory regime. J. Comput. Appl. Math. 457: 116240 (2025)- 2024
- [j59]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): 35 (2024) - [j58]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: 1-18 (2024) - [j57]Björn Bahr, Markus Faustmann, Jens Markus Melenk:
An implementation of hp-FEM for the fractional Laplacian. Comput. Math. Appl. 176: 324-348 (2024) - [j56]Chupeng Ma, Jens Markus Melenk:
Exponential Convergence of a Generalized FEM for Heterogeneous Reaction-Diffusion Equations. Multiscale Model. Simul. 22(1): 256-282 (2024) - [j55]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. Math. Comput. 94(351): 73-122 (2024) - [i37]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 abs/2401.10141 (2024) - [i36]Jens Markus Melenk, Ilaria Perugia, Alexander Rieder:
FEM-BEM coupling for the high-frequency Helmholtz problem. CoRR abs/2407.04428 (2024) - [i35]Björn Bahr, Markus Faustmann, Jens Markus Melenk:
An implementation of hp-FEM for the fractional Laplacian. CoRR abs/2407.11482 (2024) - [i34]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. CoRR abs/2407.14424 (2024) - [i33]C. Lin, Jens Markus Melenk, Stefan A. Sauter:
The Green's function for an acoustic half-space problem with impedance boundary conditions Part I: Representation formula. CoRR abs/2408.03108 (2024) - [i32]C. Lin, Jens Markus Melenk, S. Sauter:
The Green's function for an acoustic, half-space impedance problem Part II: Analysis of the slowly varying and the plane wave component. CoRR abs/2408.03587 (2024) - [i31]Jens Markus Melenk, David Wörgötter:
Regularity of vector fields with piecewise regular curl and divergence. CoRR abs/2408.16556 (2024) - [i30]Jens Markus Melenk, Jörg Nick:
Parsimonious convolution quadrature. CoRR abs/2410.15079 (2024) - 2023
- [j54]Niklas Angleitner, Markus Faustmann, Jens Markus Melenk:
ℋ-inverses for RBF interpolation. Adv. Comput. Math. 49(6): 85 (2023) - [j53]Niklas Angleitner, Markus Faustmann, Jens Markus Melenk:
Exponential meshes and H-matrices. Comput. Math. Appl. 130: 21-40 (2023) - [j52]Lehel Banjai, Jens Markus Melenk, Christoph Schwab:
Exponential convergence of hp FEM for spectral fractional diffusion in polygons. Numerische Mathematik 153(1): 1-47 (2023) - [j51]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): 2601-2622 (2023) - [i29]Michael Karkulik, Jens Markus Melenk, Alexander Rieder:
On interpolation spaces of piecewise polynomials on mixed meshes. CoRR abs/2306.16907 (2023) - [i28]Jens Markus Melenk, Leszek F. Demkowicz, Stefan Henneking:
Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides. CoRR abs/2307.04521 (2023) - [i27]Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab:
Weighted analytic regularity for the integral fractional Laplacian in polyhedra. CoRR abs/2307.11679 (2023) - [i26]Jannis Körner, Anton Arnold, Christian Klein, Jens Markus Melenk:
Optimally truncated WKB approximation for the highly oscillatory stationary 1D Schrödinger equation. CoRR abs/2310.00955 (2023) - [i25]Franz Achleitner, Goro Akagi, Christian Kuehn, Jens Markus Melenk, Jens D. M. Rademacher, Cinzia Soresina, Jichen Yang:
Fractional Dissipative PDEs. CoRR abs/2312.05606 (2023) - 2022
- [j50]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): 59 (2022) - [j49]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: 18-35 (2022) - [j48]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): 2 (2022) - [j47]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): 2165-2195 (2022) - [j46]Markus Faustmann, Jens Markus Melenk, Maryam Parvizi:
Caccioppoli-type estimates and ℋ-matrix approximations to inverses for FEM-BEM couplings. Numerische Mathematik 150(3): 849-892 (2022) - [j45]Markus Faustmann, Michael Karkulik, Jens Markus Melenk:
Local Convergence of the FEM for the Integral Fractional Laplacian. SIAM J. Numer. Anal. 60(3): 1055-1082 (2022) - [i24]Jens Markus Melenk, Stefan A. Sauter:
Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions. CoRR abs/2201.02602 (2022) - [i23]Jens Markus Melenk, Alexander Rieder:
An exponentially convergent discretization for space-time fractional parabolic equations using hp-FEM. CoRR abs/2202.02067 (2022) - [i22]Niklas Angleitner, Markus Faustmann, Jens Markus Melenk:
Exponential meshes and H-matrices. CoRR abs/2203.09925 (2022) - [i21]Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab:
Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D. CoRR abs/2204.04113 (2022) - [i20]Chupeng Ma, Jens Markus Melenk:
Exponential convergence of a generalized FEM for heterogeneous reaction-diffusion equations. CoRR abs/2209.01957 (2022) - [i19]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 abs/2209.03601 (2022) - [i18]Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab:
Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons. CoRR abs/2209.11468 (2022) - [i17]Roland Becker, Maximilian Brunner, Michael Innerberger, Jens Markus Melenk, Dirk Praetorius:
Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs. CoRR abs/2211.04123 (2022) - 2021
- [j44]Franz Achleitner, Christian Kuehn, Jens Markus Melenk, Alexander Rieder:
Metastable speeds in the fractional Allen-Cahn equation. Appl. Math. Comput. 408: 126329 (2021) - [j43]Jens Markus Melenk, Stefan A. Sauter:
Wavenumber-Explicit hp-FEM Analysis for Maxwell's Equations with Transparent Boundary Conditions. Found. Comput. Math. 21(1): 125-241 (2021) - [j42]Markus Faustmann, Jens Markus Melenk, Dirk Praetorius:
Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. Math. Comput. 90(330): 1557-1587 (2021) - [j41]Jens Markus Melenk, Alexander Rieder:
On superconvergence of Runge-Kutta convolution quadrature for the wave equation. Numerische Mathematik 147(1): 157-188 (2021) - [i16]Markus Faustmann, Jens Markus Melenk, Maryam Parvizi:
$\mathcal{H}$-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations. CoRR abs/2103.14981 (2021) - [i15]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 abs/2105.06173 (2021) - [i14]Niklas Angleitner, Markus Faustmann, Jens Markus Melenk:
H-inverses for RBF interpolation. CoRR abs/2109.05763 (2021) - [i13]Roland Becker, Maximilian Brunner, Michael Innerberger, Jens Markus Melenk, Dirk Praetorius:
Goal-oriented adaptive finite element method for semilinear elliptic PDEs. CoRR abs/2112.06687 (2021) - [i12]Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab:
Weighted analytic regularity for the integral fractional Laplacian in polygons. CoRR abs/2112.08151 (2021) - 2020
- [j40]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): 2351-2378 (2020) - [j39]Jens Markus Melenk, C. Rojik:
On commuting p-version projection-based interpolation on tetrahedra. Math. Comput. 89(321): 45-87 (2020) - [j38]Jens Markus Melenk, Stefan A. Sauter, Céline Torres:
Wavenumber Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems. SIAM J. Numer. Anal. 58(4): 2119-2143 (2020) - [i11]Alexander Rieder, Francisco-Javier Sayas, Jens Markus Melenk:
Runge-Kutta approximation for C0-semigroups in the graph norm with applications to time domain boundary integral equations. CoRR abs/2003.01996 (2020) - [i10]Lorenzo Mascotto, Jens Markus Melenk, Ilaria Perugia, Alexander Rieder:
FEM-BEM mortar coupling for the Helmholtz problem in three dimensions. CoRR abs/2004.03523 (2020) - [i9]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 abs/2004.10517 (2020) - [i8]Niklas Angleitner, Markus Faustmann, Jens Markus Melenk:
Approximating inverse FEM matrices on non-uniform meshes with $\mathcal{H}$-matrices. CoRR abs/2005.04999 (2020) - [i7]Markus Faustmann, Michael Karkulik, Jens Markus Melenk:
Local convergence of the FEM for the integral fractional Laplacian. CoRR abs/2005.14109 (2020) - [i6]Franz Achleitner, Christian Kuehn, Jens Markus Melenk, Alexander Rieder:
Metastable Speeds in the Fractional Allen-Cahn Equation. CoRR abs/2006.02731 (2020) - [i5]Markus Faustmann, Jens Markus Melenk, Maryam Parvizi:
Caccioppoli-type estimates and H-Matrix approximations to inverses for FEM-BEM couplings. CoRR abs/2008.11498 (2020) - [i4]Alexander Rieder, Francisco-Javier Sayas, Jens Markus Melenk:
Time domain boundary integral equations and convolution quadrature for scattering by composite media. CoRR abs/2010.14162 (2020) - [i3]Lehel Banjai, Jens Markus Melenk, Christoph Schwab:
Exponential Convergence of hp FEM for Spectral Fractional Diffusion in Polygons. CoRR abs/2011.05701 (2020) - [i2]Maximilian Bernkopf, Jens Markus Melenk:
Optimal convergence rates in L2 for a first order system least squares finite element method. Part I: homogeneous boundary conditions. CoRR abs/2012.12919 (2020)
2010 – 2019
- 2019
- [j37]Michael Karkulik, Jens Markus Melenk:
H-matrix approximability of inverses of discretizations of the fractional Laplacian. Adv. Comput. Math. 45(5): 2893-2919 (2019) - [j36]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): 901-962 (2019) - [i1]Markus Faustmann, Jens Markus Melenk, Maryam Parvizi:
On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion. CoRR abs/1912.09160 (2019) - 2018
- [j35]Markus Faustmann, Jens Markus Melenk:
Local convergence of the boundary element method on polyhedral domains. Numerische Mathematik 140(3): 593-637 (2018) - 2017
- [j34]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): 1576-1589 (2017) - [j33]Steffen Börm, Christina Börst, Jens Markus Melenk:
An analysis of a butterfly algorithm. Comput. Math. Appl. 74(9): 2125-2143 (2017) - [j32]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): 2651-2686 (2017) - [j31]Steffen Börm, Jens Markus Melenk:
Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis. Numerische Mathematik 137(1): 1-34 (2017) - 2016
- [j30]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): 119-152 (2016) - 2015
- [j29]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): 1583-1605 (2015) - [j28]Michael Karkulik, Jens Markus Melenk:
Local high-order regularization and applications to hp-methods. Comput. Math. Appl. 70(7): 1606-1639 (2015) - [j27]Markus Aurada, Jens Markus Melenk, Dirk Praetorius:
FEM-BEM coupling for the large-body limit in micromagnetics. J. Comput. Appl. Math. 281: 10-31 (2015) - [j26]Markus Faustmann, Jens Markus Melenk, Dirk Praetorius:
ℋ-matrix approximability of the inverses of FEM matrices. Numerische Mathematik 131(4): 615-642 (2015) - 2014
- [j25]S. Esterhazy, Jens Markus Melenk:
An analysis of discretizations of the Helmholtz equation in L2 and in negative norms. Comput. Math. Appl. 67(4): 830-853 (2014) - [j24]Jens Markus Melenk, T. Wurzer:
On the stability of the boundary trace of the polynomial L2-projection on triangles and tetrahedra. Comput. Math. Appl. 67(4): 944-965 (2014) - 2013
- [j23]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): 367-394 (2013) - [j22]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): 291-304 (2013) - [j21]Thomas Horger, Jens Markus Melenk, Barbara I. Wohlmuth:
On optimal L2 - and surface flux convergence in FEM. Comput. Vis. Sci. 16(5): 231-246 (2013) - [j20]Jens Markus Melenk, Asieh Parsania, Stefan A. Sauter:
General DG-Methods for Highly Indefinite Helmholtz Problems. J. Sci. Comput. 57(3): 536-581 (2013) - [j19]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): 629-653 (2013) - [j18]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): 1327-1348 (2013) - 2012
- [j17]Samuel Ferraz-Leite, Jens Markus Melenk, Dirk Praetorius:
Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. Numerische Mathematik 122(1): 101-131 (2012) - [j16]Jens Markus Melenk:
Mapping Properties of Combined Field Helmholtz Boundary Integral Operators. SIAM J. Math. Anal. 44(4): 2599-2636 (2012) - [j15]Jens Markus Melenk, Barbara I. Wohlmuth:
Quasi-Optimal Approximation of Surface Based Lagrange Multipliers in Finite Element Methods. SIAM J. Numer. Anal. 50(4): 2064-2087 (2012) - [c1]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: 532-539 - 2011
- [j14]Lehel Banjai, Christian Lubich, Jens Markus Melenk:
Runge-Kutta convolution quadrature for operators arising in wave propagation. Numerische Mathematik 119(1): 1-20 (2011) - [j13]Jens Markus Melenk, Stefan A. Sauter:
Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation. SIAM J. Numer. Anal. 49(3): 1210-1243 (2011) - [j12]Maike Löhndorf, Jens Markus Melenk:
Wavenumber-Explicit hp-BEM for High Frequency Scattering. SIAM J. Numer. Anal. 49(6): 2340-2363 (2011) - 2010
- [j11]Jens Markus Melenk:
On the convergence of Filon quadrature. J. Comput. Appl. Math. 234(6): 1692-1701 (2010) - [j10]Emmanuil H. Georgoulis, Edward J. C. Hall, Jens Markus Melenk:
On the Suboptimality of the p-Version Interior Penalty Discontinuous Galerkin Method. J. Sci. Comput. 42(1): 54-67 (2010) - [j9]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): 1871-1914 (2010)
2000 – 2009
- 2005
- [j8]Steffen Börm, Maike Löhndorf, Jens Markus Melenk:
Approximation of Integral Operators by Variable-Order Interpolation. Numerische Mathematik 99(4): 605-643 (2005) - [j7]Jens Markus Melenk:
hp-Interpolation of Nonsmooth Functions and an Application to hp-A posteriori Error Estimation. SIAM J. Numer. Anal. 43(1): 127-155 (2005) - 2003
- [j6]Boris N. Khoromskij, Jens Markus Melenk:
Boundary Concentrated Finite Element Methods. SIAM J. Numer. Anal. 41(1): 1-36 (2003) - 2002
- [j5]Boris N. Khoromskij, Jens Markus Melenk:
An Efficient Direct Solver for the Boundary Concentrated FEM in 2D. Computing 69(2): 91-117 (2002) - 2001
- [j4]Jens Markus Melenk, Barbara I. Wohlmuth:
On residual-based a posteriori error estimation in hp-FEM. Adv. Comput. Math. 15(1-4): 311-331 (2001) - [j3]Tim Gutzmer, Jens Markus Melenk:
Approximation orders for natural splines in arbitrary dimensions. Math. Comput. 70(234): 699-703 (2001) - 2000
- [j2]Jens Markus Melenk, N. P. Kirchner, Christoph Schwab:
Spectral Galerkin Discretization for Hydrodynamic Stability Problems. Computing 65(2): 97-118 (2000)
1990 – 1999
- 1999
- [j1]Jens Markus Melenk:
Operator adapted spectral element methods I: harmonic and generalized harmonic polynomials. Numerische Mathematik 84(1): 35-69 (1999)
Coauthor Index
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