World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
35
Citations
4231
World Ranking
2814
National Ranking
172

Peter Knabner publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Peter Knabner sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 211 publications — 66th percentile

66% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Peter Knabner D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Peter Knabner sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 35 D-Index — 25th percentile

25% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Overview

Peter Knabner is affiliated with the University of Erlangen-Nuremberg in Germany and conducts research primarily in the fields of Engineering, Computer Science, and Mathematics. Their work spans significant subfields such as Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis, Environmental Engineering, and Mechanics of Materials.

The scientist's research topics focus on advanced numerical methods and mathematical modeling, with notable emphasis on:

  • Advanced Numerical Methods in Computational Mathematics
  • Advanced Mathematical Modeling in Engineering
  • Lattice Boltzmann Simulation Studies
  • Differential Equations and Numerical Methods
  • Groundwater flow and contamination studies
  • Computational Fluid Dynamics and Aerodynamics
  • Numerical methods in engineering

Peter Knabner has contributed to several recent papers, including:

  • "Efficiency and Accuracy of Micro-Macro Models for Mineral Dissolution" (2020) published in Water Resources Research
  • "Homogenization of Two-Phase Flow in Porous Media From Pore to Darcy Scale: A Phase-Field Approach" (2021) published in Multiscale Modeling and Simulation
  • "Comparison study of phase-field and level-set method for three-phase systems including two minerals" (2022) published in Computational Geosciences
  • "Numerical benchmark study for flow in highly heterogeneous aquifers" (2020) published in Advances in Water Resources
  • "Efficiency of Micro-Macro Models for Reactive Two-Mineral Systems" (2022) published in Multiscale Modeling and Simulation

Their frequent coauthors include Lutz Angermann, Stephan Gärttner, Nadja Ray, Andreas Rupp, and Serge Kräutle.

Publication venues recurring in their work are Multiscale Modeling and Simulation, Computational Geosciences, arXiv (Cornell University), Water Resources Research, and Advances in Water Resources.

Among published books, Peter Knabner authored a title released by Springer Nature: Numerical Methods for Elliptic and Parabolic Partial Differential Equations (2021), which has been cited in relevant literature.

Best Publications

  • Numerical Methods for Elliptic and Parabolic Partial Differential Equations

    Peter Knabner;Lutz Angerman

  • Mixed finite elements for the Richards' equation: linearization procedure

    I. S. Pop;F. Radu;P. Knabner

  • Order of Convergence Estimates for an Euler Implicit, Mixed Finite Element Discretization of Richards' Equation

    Florin Radu;Iuliu Sorin Pop;Peter Knabner

  • Beyond Kozeny–Carman: Predicting the Permeability in Porous Media

    Raphael Schulz;Nadja Ray;Simon Zech;Andreas Rupp

  • Solute transport in porous media with equilibrium and non-equilibrium multiple-site adsorption : travelling waves

    van Cj Hans Duijn;P Knabner

  • Error estimates for a mixed finite element discretization of some degenerate parabolic equations

    Florin A. Radu;Iuliu Sorin Pop;Peter Knabner

  • An analysis of crystal dissolution fronts in flows through porous media part 2: incompatible boundary conditions

    van Cj Hans Duijn;P Knabner;RJ Schotting

  • Travelling waves in the transport of reactive solutes through porous media: Adsorption and binary ion exchange — Part 1

    C. J. Van Duijn;P. Knabner

  • Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods

    M. Bause;P. Knabner

  • Comparison of numerical methods for simulating strongly nonlinear and heterogeneous reactive transport problems—the MoMaS benchmark case

    Jérôme Carrayrou;Joachim Hoffmann;Peter Knabner;Serge Kräutle

  • The modeling of reactive solute transport with sorption to mobile and immobile sorbents: 1. Experimental evidence and model development

    Peter Knabner;Kai Uwe Totsche;Ingrid Kögel-Knabner

  • A new numerical reduction scheme for fully coupled multicomponent transport‐reaction problems in porous media

    S. Kräutle;P. Knabner

  • Inverse Estimation of the Unsaturated Soil Hydraulic Properties from Column Outflow Experiments Using Free-Form Parameterizations

    S. Bitterlich;W. Durner;S. C. Iden;P. Knabner

  • A reduction scheme for coupled multicomponent transport‐reaction problems in porous media: Generalization to problems with heterogeneous equilibrium reactions

    S. Kräutle;P. Knabner

  • Finite Element Approximation of the Transport of Reactive Solutes in Porous Media. Part 1: Error Estimates for Nonequilibrium Adsorption Processes

    John W. Barrett;Peter Knabner

  • Rigorous homogenization of a Stokes–Nernst–Planck–Poisson system

    A Adrian Muntean;P Knabner

  • Modeling of drug release from collagen matrices.

    Florin A. Radu;Markus Bause;Peter Knabner;Geoffrey W. Lee

  • Multiscale Approaches in Reactive Transport Modeling

    Sergi Molins;Peter Knabner

  • Reactive transport benchmark of MoMaS

    Jérôme Carrayrou;Michel Kern;Peter Knabner

  • Uniform Error Analysis for Lagrange--Galerkin Approximations of Convection-Dominated Problems

    Markus Bause;Peter Knabner

  • Multiscale Modeling of Colloid and Fluid Dynamics in Porous Media Including an Evolving Microstructure

    Nadja Ray;Tycho van Noorden;Florian Frank;Peter Knabner

  • Numerik partieller Differentialgleichungen

    Peter Knabner;Lutz Angermann

Frequent Co-Authors

Sabine Attinger
Sabine Attinger Helmholtz Centre for Environmental Research
Ioan Pop
Ioan Pop Karlsruhe Institute of Technology
Ingrid Kögel-Knabner
Ingrid Kögel-Knabner Technical University of Munich
Kai Uwe Totsche
Kai Uwe Totsche Friedrich Schiller University Jena
Harald Garcke
Harald Garcke University of Regensburg
Harry Vereecken
Harry Vereecken Forschungszentrum Jülich
John W. Barrett
John W. Barrett University of Nottingham
Gedeon Dagan
Gedeon Dagan Tel Aviv University
Wolfgang Durner
Wolfgang Durner Technische Universität Braunschweig
Kerry T.B. MacQuarrie
Kerry T.B. MacQuarrie University of New Brunswick

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