155 citations · 449 across the 12 of their papers we have counts for
13 papers
Uniform error analysis of a rectangular Morley finite element method on a Shishkin mesh for a 4th-order singularly perturbed boundary value problem
Xiangyun Meng, Martin Stynes
The singularly perturbed reaction-diffusion problem is considered on the unit square in with homoge…
Optimal balanced-norm error estimate of the LDG method for reaction-diffusion problems II: the two-dimensional case with layer-upwind flux
Yao Cheng, Xuesong Wang, Martin Stynes
A singularly perturbed reaction-diffusion problem posed on the unit square in is solved numerically by a local discontinuous Galerkin (LDG) finite element method. Ty…
A fitted scheme for a Caputo initial-boundary value problem
J. L. Gracia, E. O'Riordan, M. Stynes
In this paper we consider an initial-boundary value problem with a Caputo time derivative of order . The solution typically exhibits a weak singularity near the initial…
The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers
Yao Cheng, Martin Stynes
A singularly perturbed convection-diffusion problem,posed on the unit square in , is studied; its solution has both exponential and characteristic boundary layers. Th…
Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem
Yao Cheng, Shan Jiang, Martin Stynes
A singularly perturbed convection-diffusion problem posed on the unit square in , whose solution has exponential boundary layers, is solved numerically using the loca…
Optimal long-time decay rate of solutions of complete monotonicity-preserving schemes for nonlinear time-fractional evolutionary equations
Dongling Wang, Martin Stynes
The solution of the nonlinear initial-value problem for with , where is a Caputo derivative of order …