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In this paper a singularly perturbed reaction-diffusion partial differential equation in two space dimensions is examined. By means of an appropriate decomposition, we describe the asymptotic behaviour of the solution of problems of this kind. A central finite difference scheme is constructed for this problem which involves an appropriate Shishkin mesh. We… (More)

Keywords: Parabolic reaction–diffusion problems Semidiscrete problems Asymptotic behavior Uniform convergence Special nonuniform mesh a b s t r a c t In this work we are interested in the numerical approximation of 1D parabolic singularly perturbed problems of reaction–diffusion type. To approximate the multiscale solution of this problem we use a numerical… (More)

Keywords: Parabolic reaction–diffusion problems Hybrid method Uniform convergence High order Vulanovic´mesh a b s t r a c t This paper deals with the numerical approximation of the solution of 1D parabolic singularly perturbed problems of reaction–diffusion type. The numerical method combines the standard implicit Euler method on a uniform mesh to… (More)

SUMMARY In this paper we present efficient multigrid methods for systems of partial differential equations that are governed by a dominating grad-div operator. In particular, we show that distributive smoothing methods give multigrid convergence factors that are independent of problem parameters and of the mesh sizes in space and time. The applications… (More)

We are interested in the design of efficient geometric multigrid methods on hierarchical triangular grids for problems in two dimensions. Fourier analysis is a well-known useful tool in multigrid for the prediction of two-grid convergence rates which has been used mainly for rectangular–grids. This analysis can be extended straightforwardly to triangular… (More)