Martin Stynes

Publication Activity (10 Years)

Years Active: 1994-2024
Publications (10 Years): 56

Top Topics

Diffusion Equation

Boundary Value Problem

Top Venues

J. Sci. Comput.

Adv. Comput. Math.

J. Comput. Appl. Math.

Publications

Xiangyun Meng, Martin Stynes
Balanced and energy norm error bounds for a spatial FEM with Crank-Nicolson and BDF2 time discretisation applied to a singularly perturbed reaction-diffusion problem. Numer. Algorithms 95 (3) (2024)
Yao Cheng, Xuesong Wang, Martin Stynes
Optimal Balanced-Norm Error Estimate of the LDG Method for Reaction-Diffusion Problems I: The One-Dimensional Case. J. Sci. Comput. 100 (2) (2024)
Yongtao Zhou, Cui Li, Martin Stynes
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation. Numer. Algorithms 95 (2) (2024)
Minghua Chen, Weihua Deng, Chao Min, Jiankang Shi, Martin Stynes
Error analysis of a collocation method on graded meshes for a fractional Laplacian problem. Adv. Comput. Math. 50 (3) (2024)
Zheng Ma, Martin Stynes
Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent. J. Sci. Comput. 100 (2) (2024)
Yongtao Zhou, Hongyu Qin, Martin Stynes
An α-robust error analysis of the L1‾ scheme for time-fractional integro-differential initial-boundary value problems. Comput. Math. Appl. 162 (2024)
José Luis Gracia, Martin Stynes
A collocation method for an RLC fractional derivative two-point boundary value problem with a singular solution. Comput. Appl. Math. 43 (4) (2024)
Yao Cheng, Xuesong Wang, Martin Stynes
Optimal balanced-norm error estimate of the LDG method for reaction-diffusion problems II: the two-dimensional case with layer-upwind flux. CoRR (2024)
José Luis Gracia, Eugene O'Riordan, Martin Stynes
A fitted scheme for a Caputo initial-boundary value problem. CoRR (2024)
Dongling Wang, Martin Stynes
Optimal Long-Time Decay Rate of Numerical Solutions for Nonlinear Time-Fractional Evolutionary Equations. SIAM J. Numer. Anal. 61 (5) (2023)
Yao Cheng, Martin Stynes
The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers. Numerische Mathematik 154 (1-2) (2023)
Yao Cheng, Shan Jiang, Martin Stynes
Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem. Math. Comput. 92 (343) (2023)
Enyu Fan, Changpin Li, Martin Stynes
Discretised general fractional derivative. Math. Comput. Simul. 208 (2023)
Martin Stynes, Dongling Wang
A sharp discrete convolution sum estimate. Commun. Nonlinear Sci. Numer. Simul. 117 (2023)
Natalia Kopteva, Martin Stynes
A posteriori error analysis for variable-coefficient multiterm time-fractional subdiffusion equations. CoRR (2022)
Yao Cheng, Martin Stynes
The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers. CoRR (2022)
Xiangyun Meng, Martin Stynes
Balanced-Norm and Energy-Norm Error Analyses for a Backward Euler/FEM Solving a Singularly Perturbed Parabolic Reaction-Diffusion Problem. J. Sci. Comput. 92 (2) (2022)
Hu Chen, Martin Stynes
Using Complete Monotonicity to Deduce Local Error Estimates for Discretisations of a Multi-Term Time-Fractional Diffusion Equation. Comput. Methods Appl. Math. 22 (1) (2022)
Yongtao Zhou, Martin Stynes
Block boundary value methods for solving linear neutral Volterra integro-differential equations with weakly singular kernels. J. Comput. Appl. Math. 401 (2022)
Dongling Wang, Martin Stynes
Optimal long-time decay rate of solutions of complete monotonicity-preserving schemes for nonlinear time-fractional evolutionary equations. CoRR (2022)
Yao Cheng, Shan Jiang, Martin Stynes
Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem. CoRR (2022)
Natalia Kopteva, Martin Stynes
A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations. J. Sci. Comput. 92 (2) (2022)
Chaobao Huang, Martin Stynes
Scheme and a Standard FEM. J. Sci. Comput. 91 (2) (2022)
José Luis Gracia, Martin Stynes
A finite difference method for an initial-boundary value problem with a Riemann-Liouville-Caputo spatial fractional derivative. J. Comput. Appl. Math. 381 (2021)
Jinye Shen, Martin Stynes, Zhi-Zhong Sun
Two Finite Difference Schemes for Multi-Dimensional Fractional Wave Equations with Weakly Singular Solutions. Comput. Methods Appl. Math. 21 (4) (2021)
Chaobao Huang, Martin Stynes
α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation. Numer. Algorithms 87 (4) (2021)
Kim-Ngan Le, Martin Stynes
An α-Robust Semidiscrete Finite Element Method for a Fokker-Planck Initial-Boundary Value Problem with Variable-Order Fractional Time Derivative. J. Sci. Comput. 86 (2) (2021)
Chaobao Huang, Martin Stynes, Hu Chen
An α-robust finite element method for a multi-term time-fractional diffusion problem. J. Comput. Appl. Math. 389 (2021)
Lin Wang, Martin Stynes
-robust finite difference method for a time-fractional radially symmetric diffusion problem. Comput. Math. Appl. 97 (2021)
Chaobao Huang, Martin Stynes
Optimal spatial H1-norm analysis of a finite element method for a time-fractional diffusion equation. J. Comput. Appl. Math. 367 (2020)
Chaobao Huang, Martin Stynes
Superconvergence of a Finite Element Method for the Multi-term Time-Fractional Diffusion Problem. J. Sci. Comput. 82 (1) (2020)
Hu Chen, Martin Stynes
A discrete comparison principle for the time-fractional diffusion equation. Comput. Math. Appl. 80 (5) (2020)
Xiangyun Meng, Martin Stynes
Barrier Function Local and Global Analysis of an L1 Finite Element Method for a Multiterm Time-Fractional Initial-Boundary Value Problem. J. Sci. Comput. 84 (1) (2020)
Chaobao Huang, Xiaohui Liu, Xiangyun Meng, Martin Stynes
Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem. Comput. Methods Appl. Math. 20 (4) (2020)
Chaobao Huang, Martin Stynes
Error analysis of a finite element method with GMMP temporal discretisation for a time-fractional diffusion equation. Comput. Math. Appl. 79 (9) (2020)
Chaobao Huang, Martin Stynes
spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation. Adv. Comput. Math. 46 (4) (2020)
Guanglong Ma, Martin Stynes
A direct discontinuous Galerkin finite element method for convection-dominated two-point boundary value problems. Numer. Algorithms 83 (2) (2020)
Hui Liang, Martin Stynes
Collocation methods for general Riemann-Liouville two-point boundary value problems. Adv. Comput. Math. 45 (2) (2019)
Xiangyun Meng, Martin Stynes
Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions. Adv. Comput. Math. 45 (2) (2019)
Stephen Russell, Martin Stynes
Balanced-norm error estimates for sparse grid finite element methods applied to singularly perturbed reaction-diffusion problems. J. Num. Math. 27 (1) (2019)
Hu Chen, Martin Stynes
Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem. J. Sci. Comput. 79 (1) (2019)
Hu Chen, Martin Stynes
A High Order Method on Graded Meshes for a Time-Fractional Diffusion Problem. FDM (2018)
Thái Anh Nhan, Martin Stynes, Relja Vulanovic
Optimal uniform-convergence results for convection-diffusion problems in one dimension using preconditioning. J. Comput. Appl. Math. 338 (2018)
José Luis Gracia, Eugene O'Riordan, Martin Stynes
Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem. Comput. Methods Appl. Math. 18 (1) (2018)
Martin Stynes
Fractional-order derivatives defined by continuous kernels are too restrictive. Appl. Math. Lett. 85 (2018)
Hui Liang, Martin Stynes
Collocation Methods for General Caputo Two-Point Boundary Value Problems. J. Sci. Comput. 76 (1) (2018)
Jose L. Gracia, Eugene O'Riordan, Martin Stynes
A Fitted Scheme for a Caputo Initial-Boundary Value Problem. J. Sci. Comput. 76 (1) (2018)
Martin Stynes, Eugene O'Riordan, José Luis Gracia
Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation. SIAM J. Numer. Anal. 55 (2) (2017)
Natalia Kopteva, Martin Stynes
Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem. Adv. Comput. Math. 43 (1) (2017)
Martin Stynes, José Luis Gracia
Preprocessing schemes for fractional-derivative problems to improve their convergence rates. Appl. Math. Lett. 74 (2017)
Can Huang, Martin Stynes
A spectral collocation method for a weakly singular Volterra integral equation of the second kind. Adv. Comput. Math. 42 (5) (2016)
José Luis Gracia, Eugene O'Riordan, Martin Stynes
Convergence Outside the Initial Layer for a Numerical Method for the Time-Fractional Heat Equation. NAA (2016)
Hans-Görg Roos, Martin Stynes
Some Open Questions in the Numerical Analysis of Singularly Perturbed Differential Equations. Comput. Methods Appl. Math. 15 (4) (2015)
Jose L. Gracia, Martin Stynes
Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems. J. Comput. Appl. Math. 273 (2015)
Martin Stynes, José Luis Gracia
Boundary Layers in a Two-Point Boundary Value Problem with a Caputo Fractional Derivative. Comput. Methods Appl. Math. 15 (1) (2015)
Runchang Lin, Martin Stynes
A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems. Numer. Algorithms 70 (4) (2015)
Martin Stynes
Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements. Math. Comput. 83 (290) (2014)
Sebastian Franz, R. Bruce Kellogg, Martin Stynes
Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities. Math. Comput. 81 (278) (2012)
Runchang Lin, Martin Stynes
A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems. SIAM J. Numer. Anal. 50 (5) (2012)
Natalia Kopteva, Martin Stynes
Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem. Numerische Mathematik 119 (4) (2011)
Fang Liu, Martin Stynes, Aihui Zhou
Postprocessed Two-Scale Finite Element Discretizations, Part I. SIAM J. Numer. Anal. 49 (5) (2011)
Carmelo Clavero, Jose L. Gracia, Martin Stynes
A simpler analysis of a hybrid numerical method for time-dependent convection-diffusion problems. J. Comput. Appl. Math. 235 (17) (2011)
Eugene O'Riordan, Martin Stynes
Numerical analysis of a strongly coupled system of two singularly perturbed convection-diffusion problems. Adv. Comput. Math. 30 (2) (2009)
Aidan Naughton, Martin Stynes
Singularly Perturbed Convection - Diffusion Problems in One Dimension: Bounds on Derivatives. Comput. Methods Appl. Math. 9 (3) (2009)
Torsten Linß, Martin Stynes
Numerical Solution of Systems of Singularly Perturbed Differential Equations. Comput. Methods Appl. Math. 9 (2) (2009)
Eugene O'Riordan, Jeanne Stynes, Martin Stynes
An Iterative Numerical Algorithm for a Strongly Coupled System of Singularly Perturbed Convection-Diffusion Problems. NAA (2008)
R. Bruce Kellogg, Torsten Linß, Martin Stynes
A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions. Math. Comput. 77 (264) (2008)
R. Bruce Kellogg, Martin Stynes
Sharpened bounds for corner singularities and boundary layers in a simple convection-diffusion problem. Appl. Math. Lett. 20 (5) (2007)
Martin Stynes
Convection-diffusion-reaction problems, SDFEM/SUPG and a priori meshes. Int. J. Comput. Sci. Math. 1 (2/3/4) (2007)
Martin Stynes, Natalia Kopteva
Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions. Comput. Math. Appl. 51 (5) (2006)
Natalia Kopteva, Niall Madden, Martin Stynes
Grid equidistribution for reaction-diffusion problems in one dimension. Numer. Algorithms 40 (3) (2005)
Martin Stynes, Lutz Tobiska
The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy. SIAM J. Numer. Anal. 41 (5) (2003)
R. Bruce Kellogg, Martin Stynes
-Widths and Singularly Perturbed Boundary Value Problems II. SIAM J. Numer. Anal. 39 (2) (2001)
Natalia Kopteva, Martin Stynes
A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem. SIAM J. Numer. Anal. 39 (4) (2001)
Torsten Linß, Martin Stynes
The sdfem on Shishkin meshes for linear convection-diffusion problems. Numerische Mathematik 87 (3) (2001)
Martin Stynes, Lutz Tobiska
Analysis of the streamline-diffusion finite element method on a piecewise uniform mesh for a convection-diffusion problem with exponential layers. J. Num. Math. 9 (1) (2001)
Martin Stynes, Lutz Tobiska
A finite difference analysis of a streamline diffusion method on a Shishkin mesh. Numer. Algorithms 18 (3-4) (1998)
Wen Guo, Martin Stynes
An analysis of a cell-vertex finite volume method for a parabolic convection-diffusion problem. Math. Comput. 66 (217) (1997)
K. W. Morton, Martin Stynes, Endre Süli
Analysis of a cell-vertex finite volume method for convection-diffusion problems. Math. Comput. 66 (220) (1997)
Guangfu Sun, Martin Stynes
A uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions. Math. Comput. 65 (215) (1996)
D. Adam, A. Felgenhauer, Hans-Görg Roos, Martin Stynes
A Nonconforming Finite Element Method for a Singularly Petrurbed Boundary Value Problem. Computing 54 (1) (1995)
Guangfu Sun, Martin Stynes
Finite element methods on piecewise equidistant meshes for interior turning point problems. Numer. Algorithms 8 (1) (1994)