A Finite Element Method for a Singularly Perturbed Boundary Value Problem.
Finite element analyis of exponentially fitted Lumped schemes for time-dependent convection-diffusion problems.
L1 and L... Uniform Convergence of a Difference Scheme for a Semilinear Singular Perturbation Problem.
Uniformly Convergent Difference Schemes for Singularly Perturbed Parabolic Diffusion-Convection Problems Without Turning Points.
Necessary conditions for uniform convergence of finite difference schemes for convection-diffusion problems with exponential and parabolic layers
Singularly perturbed problems of convection-diffusion type cannot be solved numerically in a completely satisfactory manner by standard numerical methods. This indicates the need for robust or -uniform methods. In this paper we derive new conditions for such schemes with special emphasize to parabolic layers.
-widths for singularly perturbed problems
Kolmogorov -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
A curious property of oscillatory FEM solutions of one-dimensional convection-diffusion problems
Song, Yin and Zhang (Int. J. Numer. Anal. Model. 4: 127-140, 2007) discovered a remarkable property of oscillatory finite element solutions of one-dimensional convection-diffusion problems that leads to a novel numerical method for the solution of such problems. In the present paper this property is described using several figures, then a simple proof of the phenomenon is given which is much more intuitive than the technical analysis of Song et al.
The combination technique for a two-dimensional convection-diffusion problem with exponential layers
Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing for the maximum number of mesh intervals in each coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin FEM on , and meshes. It is shown that the combination FEM yields (up to a factor ) the same order of accuracy in the associated...
-widths for singularly perturbed problems
Page 1