Martin Stynes
Orcid: 0000-0003-2085-7354
According to our database1,
Martin Stynes
authored at least 72 papers
between 1994 and 2024.
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Bibliography
2024
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, March, 2024
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation.
Numer. Algorithms, February, 2024
2023
Optimal Long-Time Decay Rate of Numerical Solutions for Nonlinear Time-Fractional Evolutionary Equations.
SIAM J. Numer. Anal., October, 2023
The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers.
Numerische Mathematik, June, 2023
Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem.
Math. Comput., April, 2023
Commun. Nonlinear Sci. Numer. Simul., 2023
2022
Balanced-Norm and Energy-Norm Error Analyses for a Backward Euler/FEM Solving a Singularly Perturbed Parabolic Reaction-Diffusion Problem.
J. Sci. Comput., 2022
A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations.
J. Sci. Comput., 2022
A Sharp α-Robust L<sup>∞</sup> (H<sup>1)</sup> Error Bound for a Time-Fractional Allen-Cahn Problem Discretised by the Alikhanov L2-1<sub>σ</sub> Scheme and a Standard FEM.
J. Sci. Comput., 2022
Block boundary value methods for solving linear neutral Volterra integro-differential equations with weakly singular kernels.
J. Comput. Appl. Math., 2022
Optimal long-time decay rate of solutions of complete monotonicity-preserving schemes for nonlinear time-fractional evolutionary equations.
CoRR, 2022
Using Complete Monotonicity to Deduce Local Error Estimates for Discretisations of a Multi-Term Time-Fractional Diffusion Equation.
Comput. Methods Appl. Math., 2022
2021
α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation.
Numer. Algorithms, 2021
An α-Robust Semidiscrete Finite Element Method for a Fokker-Planck Initial-Boundary Value Problem with Variable-Order Fractional Time Derivative.
J. Sci. Comput., 2021
An α-robust finite element method for a multi-term time-fractional diffusion problem.
J. Comput. Appl. Math., 2021
A finite difference method for an initial-boundary value problem with a Riemann-Liouville-Caputo spatial fractional derivative.
J. Comput. Appl. Math., 2021
Two Finite Difference Schemes for Multi-Dimensional Fractional Wave Equations with Weakly Singular Solutions.
Comput. Methods Appl. Math., 2021
An <i>α</i>-robust finite difference method for a time-fractional radially symmetric diffusion problem.
Comput. Math. Appl., 2021
2020
A direct discontinuous Galerkin finite element method for convection-dominated two-point boundary value problems.
Numer. Algorithms, 2020
Barrier Function Local and Global Analysis of an L1 Finite Element Method for a Multiterm Time-Fractional Initial-Boundary Value Problem.
J. Sci. Comput., 2020
Superconvergence of a Finite Element Method for the Multi-term Time-Fractional Diffusion Problem.
J. Sci. Comput., 2020
Optimal spatial H1-norm analysis of a finite element method for a time-fractional diffusion equation.
J. Comput. Appl. Math., 2020
Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem.
Comput. Methods Appl. Math., 2020
Error analysis of a finite element method with GMMP temporal discretisation for a time-fractional diffusion equation.
Comput. Math. Appl., 2020
Comput. Math. Appl., 2020
Optimal H<sup>1</sup> spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation.
Adv. Comput. Math., 2020
2019
Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem.
J. Sci. Comput., 2019
Balanced-norm error estimates for sparse grid finite element methods applied to singularly perturbed reaction-diffusion problems.
J. Num. Math., 2019
Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions.
Adv. Comput. Math., 2019
Adv. Comput. Math., 2019
2018
J. Sci. Comput., 2018
Optimal uniform-convergence results for convection-diffusion problems in one dimension using preconditioning.
J. Comput. Appl. Math., 2018
Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem.
Comput. Methods Appl. Math., 2018
Appl. Math. Lett., 2018
Proceedings of the Finite Difference Methods. Theory and Applications, 2018
2017
Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation.
SIAM J. Numer. Anal., 2017
Preprocessing schemes for fractional-derivative problems to improve their convergence rates.
Appl. Math. Lett., 2017
Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem.
Adv. Comput. Math., 2017
2016
A spectral collocation method for a weakly singular Volterra integral equation of the second kind.
Adv. Comput. Math., 2016
Convergence Outside the Initial Layer for a Numerical Method for the Time-Fractional Heat Equation.
Proceedings of the Numerical Analysis and Its Applications - 6th International Conference, 2016
2015
A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems.
Numer. Algorithms, 2015
Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems.
J. Comput. Appl. Math., 2015
Boundary Layers in a Two-Point Boundary Value Problem with a Caputo Fractional Derivative.
Comput. Methods Appl. Math., 2015
Some Open Questions in the Numerical Analysis of Singularly Perturbed Differential Equations.
Comput. Methods Appl. Math., 2015
2014
Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements.
Math. Comput., 2014
2012
A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems.
SIAM J. Numer. Anal., 2012
Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities.
Math. Comput., 2012
2011
SIAM J. Numer. Anal., 2011
Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem.
Numerische Mathematik, 2011
A simpler analysis of a hybrid numerical method for time-dependent convection-diffusion problems.
J. Comput. Appl. Math., 2011
2009
Singularly Perturbed Convection - Diffusion Problems in One Dimension: Bounds on Derivatives.
Comput. Methods Appl. Math., 2009
Comput. Methods Appl. Math., 2009
Numerical analysis of a strongly coupled system of two singularly perturbed convection-diffusion problems.
Adv. Comput. Math., 2009
2008
A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions.
Math. Comput., 2008
An Iterative Numerical Algorithm for a Strongly Coupled System of Singularly Perturbed Convection-Diffusion Problems.
Proceedings of the Numerical Analysis and Its Applications, 4th International Conference, 2008
2007
Int. J. Comput. Sci. Math., 2007
Sharpened bounds for corner singularities and boundary layers in a simple convection-diffusion problem.
Appl. Math. Lett., 2007
2006
Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions.
Comput. Math. Appl., 2006
2005
Numer. Algorithms, 2005
2003
The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy.
SIAM J. Numer. Anal., 2003
2001
A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem.
SIAM J. Numer. Anal., 2001
SIAM J. Numer. Anal., 2001
Numerische Mathematik, 2001
Analysis of the streamline-diffusion finite element method on a piecewise uniform mesh for a convection-diffusion problem with exponential layers.
J. Num. Math., 2001
1998
Numer. Algorithms, 1998
1997
Math. Comput., 1997
An analysis of a cell-vertex finite volume method for a parabolic convection-diffusion problem.
Math. Comput., 1997
1996
A uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions.
Math. Comput., 1996
1995
A Nonconforming Finite Element Method for a Singularly Petrurbed Boundary Value Problem.
Computing, 1995
1994
Finite element methods on piecewise equidistant meshes for interior turning point problems.
Numer. Algorithms, 1994