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Mathematics

D-Index
47
Citations
13319
World Ranking
1242
National Ranking
67

Overview

Martin Stynes is affiliated with the Beijing Computational Science Research Center in China. Their research primarily focuses on mathematics and engineering, with a significant emphasis on numerical analysis, modeling and simulation, computational mechanics, applied mathematics, and computational theory and mathematics.

The scientist's work covers key topics including differential equations and numerical methods, fractional differential equations solutions, advanced numerical methods in computational mathematics, advanced mathematical modeling in engineering, numerical methods for differential equations, numerical methods in engineering, and nonlinear differential equations analysis.

Martin Stynes has published extensively in various academic venues. Frequent publication outlets for their research include:

  • Journal of Scientific Computing
  • arXiv (Cornell University)
  • Journal of Computational and Applied Mathematics
  • Numerical Algorithms
  • Computational Methods in Applied Mathematics

The scientist has collaborated regularly with several coauthors, notable frequent collaborators being:

  • Chaobao Huang
  • Xiangyun Meng
  • Yongtao Zhou
  • Yao Cheng
  • Hu Chen

Recent papers by Martin Stynes include:

  • "Blow-up of error estimates in time-fractional initial-boundary value problems," 2020, IMA Journal of Numerical Analysis
  • "Good (and Not So Good) Practices in Computational Methods for Fractional Calculus," 2020, Mathematics
  • "α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation," 2020, Numerical Algorithms
  • "Superconvergence of a Finite Element Method for the Multi-term Time-Fractional Diffusion Problem," 2020, Journal of Scientific Computing
  • "Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem," 2020, Computational Methods in Applied Mathematics

Best Publications

  • Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems

    Hans-Görg Roos;M. Stynes;L. Tobiska

  • Numerical Methods for Singularly Perturbed Differential Equations

    Hans-Görg Roos;Martin Stynes;Lutz Tobiska

  • Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

    Martin Stynes;Eugene O'Riordan;José Luis Gracia

  • Numerical methods for singularly perturbed differential equations : convection-diffusion and flow problems

    Hans-Görg Roos;M. Stynes;L. Tobiska

  • Numerical Treatment of Partial Differential Equations

    Christian Grossmann;Hans-Gorg Roos;Martin Stynes

  • Steady-state convection-diffusion problems

    Martin Stynes

  • Why fractional derivatives with nonsingular kernels should not be used

    Kai Diethelm;Roberto Garrappa;Andrea Giusti;Martin Stynes

  • The midpoint upwind scheme

    Martin Stynes;Hans-Görg Roos

  • A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem

    Natalia Kopteva;Martin Stynes

  • Too much regularity may force too much uniqueness

    Martin Stynes

  • Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem

    Torsten Linß;Martin Stynes

  • A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem

    Martin Stynes;Eugene O'Riordan

  • A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction–diffusion problems

    Niall Madden;Martin Stynes

  • On the Stability of Residual-Free Bubbles for Convection-Diffusion Problemsand their Approximation by a Two-Level Finite Element Method.

    L. P. Franca;A. Nesliturk;M. Stynes

  • Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem

    Hu Chen;Martin Stynes

  • The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy

    Martin Stynes;Lutz Tobiska

  • A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems

    Runchang Lin;Martin Stynes

  • A uniformly accurate finite-element method for a singularly perturbed one-dimensional reaction-diffusion

    Eugene O'Riordan;Martin Stynes

  • Corner singularities and boundary layers in a simple convection–diffusion problem☆

    R. Bruce Kellogg;Martin Stynes

  • A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions

    Eugene O’Riordan;Martin Stynes

Frequent Co-Authors

Eugene O'Riordan
Eugene O'Riordan Dublin City University
Lutz Tobiska
Lutz Tobiska Otto-von-Guericke University Magdeburg
R. Bruce Kellogg
R. Bruce Kellogg University of South Carolina
Kai Diethelm
Kai Diethelm Technische Universität Braunschweig
Endre Süli
Endre Süli University of Oxford

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