Layer-adapted meshes for time-dependent reaction-diffusion problems

Two-grid algorithms for singularly perturbed reaction-diffusion problems on layer adapted meshes

We propose a new two-grid approach based on Bellman-Kalaba quasilinearization [6] and Axelsson [4]-Xu [30] finite element two-grid method for the solution of singularly perturbed reaction-diffusion equations. The algorithms involve solving one inexpensive problem on coarse grid and solving on fine grid one linear problem obtained by quasilinearization of the differential equation about an inter...

A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions

An elliptic system of M(≥ 2) singularly perturbed linear reactiondiffusion equations, coupled through their zero-order terms, is considered on the unit square. This system does not in general satisfy a maximum principle. It is solved numerically using a standard difference scheme on tensor-product Bakhvalov and Shishkin meshes. An error analysis for these numerical methods shows that one obtain...

Local projection stabilisation on layer-adapted meshes for convection-diffusion problems with characteristic layers (Part I and II)

For a singularly perturbed convection-diffusion problem with exponential and characteristic boundary layers on the unit square a discretisation based on layer-adapted meshes is considered. The standard Galerkin method and the local projection scheme are analysed for a general class of higher order finite elements based on local polynomial spaces lying between Pp and Qp. We will present two diff...

Exponentially-fitted methods on layer-adapted meshes

In this paper, a new derivation of a uniformly-convergent, second-order method for singularly-perturbed, linear ordinary differential equations based on the freezing of the coefficients of the differential equation, and integration of the resulting equations subject to continuity and smoothness conditions at the nodes, is presented. The derivation presented here is compared with others based on...

hp-DGFEM on Shape-Irregular Meshes: Reaction-Diffusion Problems