Martin Stynes focuses on Mathematical analysis, Singular perturbation, Convection–diffusion equation, Finite difference method and Boundary value problem. In Mathematical analysis, Martin Stynes works on issues like Discontinuous Galerkin method, which are connected to Mixed finite element method. His studies deal with areas such as Elliptic curve and Reaction–diffusion system as well as Singular perturbation.
His Convection–diffusion equation research is multidisciplinary, incorporating perspectives in Numerical solution of the convection–diffusion equation, Differential operator and Unit square. He combines subjects such as Discretization, Fractional calculus, Numerical analysis and Boundary with his study of Finite difference method. In his research on the topic of Boundary value problem, Boundary layer, Interval and Scheme is strongly related with Upwind scheme.
Martin Stynes mainly focuses on Mathematical analysis, Boundary value problem, Numerical analysis, Convection–diffusion equation and Singular perturbation. His work in the fields of Mathematical analysis, such as Finite difference method, Norm, Piecewise and Differential equation, intersects with other areas such as Uniform convergence. His Boundary value problem research includes themes of Upwind scheme, Reaction–diffusion system, Fractional calculus, Applied mathematics and Boundary layer.
His Numerical analysis research is multidisciplinary, incorporating elements of Differential operator, Finite difference, Derivative, Discretization and Maximum principle. The study incorporates disciplines such as Unit square, Boundary, Galerkin method and Exponential function in addition to Convection–diffusion equation. His research investigates the connection with Singular perturbation and areas like Method of matched asymptotic expansions which intersect with concerns in Asymptotic expansion.
The scientist’s investigation covers issues in Applied mathematics, Fractional calculus, Boundary value problem, Mathematical analysis and Singularity. He has included themes like Discretization, Superconvergence, Norm and Piecewise in his Applied mathematics study. The various areas that Martin Stynes examines in his Fractional calculus study include Zero, Integer, Numerical analysis and Bounded function.
His study in Boundary value problem is interdisciplinary in nature, drawing from both Volterra integral equation, Green's function, Collocation method and Discontinuous Galerkin method. He integrates several fields in his works, including Mathematical analysis and Multi dimensional. His Singularity research incorporates themes from Pointwise, Polygon mesh and Time derivative.
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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.
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.
Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
Martin Stynes;Eugene O'Riordan;José Luis Gracia.
SIAM Journal on Numerical Analysis (2017)
Steady-state convection-diffusion problems
Acta Numerica (2005)
The midpoint upwind scheme
Martin Stynes;Hans-Görg Roos.
Applied Numerical Mathematics (1997)
A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem
Natalia Kopteva;Martin Stynes.
SIAM Journal on Numerical Analysis (2001)
Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem
Torsten Linß;Martin Stynes.
Journal of Mathematical Analysis and Applications (2001)
A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction–diffusion problems
Niall Madden;Martin Stynes.
Ima Journal of Numerical Analysis (2003)
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