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Jens Markus Melenk

Jens Markus Melenk

D-Index & Metrics

Mathematics

D-Index
36
Citations
13360
World Ranking
2570
National Ranking
32

Overview

Jens Markus Melenk is affiliated with TU Wien in Austria and focuses on research primarily in the fields of engineering, mathematics, and computer science. Their work spans several subfields including mechanics of materials, computational theory and mathematics, computational mechanics, atomic and molecular physics, and optics, as well as electrical and electronic engineering.

The core topics addressed in their research encompass advanced mathematical modeling in engineering, numerical methods in engineering, advanced numerical methods in computational mathematics, electromagnetic simulation and numerical methods, electromagnetic scattering and analysis, differential equations and numerical methods, and numerical methods in inverse problems.

Recent publications by Melenk include:

  • hp-FEM for the fractional heat equation, 2020, IMA Journal of Numerical Analysis
  • Local Convergence of the FEM for the Integral Fractional Laplacian, 2022, SIAM Journal on Numerical Analysis
  • Weighted Analytic Regularity for the Integral Fractional Laplacian in Polygons, 2022, SIAM Journal on Mathematical Analysis
  • Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs, 2022, Computers & Mathematics with Applications
  • FEM-BEM mortar coupling for the Helmholtz problem in three dimensions, 2020, BOA (University of Milano-Bicocca)

Melenk frequently publishes in venues such as arXiv (Cornell University), Computers & Mathematics with Applications, SIAM Journal on Numerical Analysis, IMA Journal of Numerical Analysis, and ESAIM. Mathematical Modelling and Numerical Analysis.

Collaborations form a significant part of their research production. Frequent co-authors include:

  • Markus Faustmann
  • Alexander Rieder
  • Christoph Schwab
  • Carlo Marcati
  • Stefan Sauter

Best Publications

  • The partition of unity finite element method: Basic theory and applications

    J. M. Melenk;Ivo M Babuska

  • The Partition of Unity Method

    Ivo M Babuska;J. M. Melenk

  • The partition of unity finite element method

    I. Babuska;J. M. Melenk

  • On residual-based a posteriori error estimation in hp -FEM

    Jens Markus Melenk;Barbara I. Wohlmuth

  • Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation

    J. M. Melenk;S. Sauter

  • Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions

    Jens Markus Melenk;Stefan A. Sauter

  • Optimal a priori estimates for higher order finite elements for elliptic interface problems

    Jingzhi Li;Jens Markus Melenk;Barbara Wohlmuth;Jun Zou

  • hp-Finite Element Methods for Singular Perturbations

    Jens M. Melenk

  • Local high-order regularization and applications to hp-methods

    M. Karkulik;J.M. Melenk

  • Fully discrete hp-finite elements: fast quadrature

    J. M. Melenk;Klaus Gerdes;C. Schwab

  • An adaptive strategy for hp-FEM based on testing for analyticity

    Tino Eibner;Jens Markus Melenk

  • On Stability of Discretizations of the Helmholtz Equation

    S. Esterhazy;J. M. Melenk

  • Runge–Kutta convolution quadrature for operators arising in wave propagation

    Lehel Banjai;Christian Lubich;Jens Markus Melenk

  • General DG-Methods for Highly Indefinite Helmholtz Problems

    J. M. Melenk;A. Parsania;S. Sauter

  • Approximation with harmonic and generalized harmonic polynomials in the partition of unity method

    J. M. Melenk;I. Babuška

  • Tensor FEM for Spectral Fractional Diffusion

    Lehel Banjai;Jens Markus Melenk;Ricardo H. Nochetto;Enrique Otárola

  • Quasi-optimal convergence rate for an adaptive boundary element method

    Michael Feischl;Michael Karkulik;Jens Markus Melenk;Dirk Praetorius

  • Approximation of Integral Operators by Variable-Order Interpolation

    Steffen Börm;Maike Löhndorf;Jens M. Melenk

  • hp FEM for Reaction-Diffusion Equations I: Robust Exponential Convergence

    J. M. Melenk;C. Schwab

  • On n-widths for elliptic problems

    J.M. Melenk

  • On Stability of Discretizations of the Helmholtz Equation (extended version)

    Sofi Esterhazy;Jens Markus Melenk

  • Institute for Analysis and Scientific Computing

    Anton Arnold;Jens Markus Melenk

Frequent Co-Authors

Stefan A. Sauter
Stefan A. Sauter University of Zurich
Barbara Wohlmuth
Barbara Wohlmuth Technical University of Munich
Ivo Babuška
Ivo Babuška The University of Texas at Austin
Ivan G. Graham
Ivan G. Graham University of Bath
Ricardo H. Nochetto
Ricardo H. Nochetto University of Maryland, College Park
Boris N. Khoromskij
Boris N. Khoromskij Max Planck Institute for Mathematics in the Sciences
Dominik Schötzau
Dominik Schötzau University of British Columbia

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