DMCA
Exponentially Fitted Hierarchical Bases Multigrid for the Convection-Diffusion Equation (1996)
BibTeX
@MISC{Küther96exponentiallyfitted,
author = {Marc Küther},
title = {Exponentially Fitted Hierarchical Bases Multigrid for the Convection-Diffusion Equation},
year = {1996}
}
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Abstract
In this paper we construct hierarchical bases for an exponentially fitted finite element discretisation of the one-dimensional stationary convection-diffusion equation. Then we prove the approximation and smoothing property of the corresponding Hierarchical Bases twogrid method [BDY88]. Key words: Hierarchical Bases Multigrid method, exponentially fitted schemes, convectiondiffusion equation. 0 Introduction. In this paper we consider the one-dimensional stationary convection-diffusion equation with homogeneous boundary conditions L " u j \Gamma"u 00 + bu 0 + cu = f in (0; 1); (0.1) u(0) = 0 = u(1): The coefficients and the right-hand-side are supposed to satisfy b 2 L 1 (0; 1); ess inf (0;1) b fi ? 0; c 2 L 1 (0; 1); ess inf (0;1) c 0; (0.2) f 2 L 1 (0; 1): Under these conditions problem (0.1) has a unique solution in W 2;1 (0; 1), the Sobolev space of twice weakly differentiable functions which are integrable up to their second derivative. It is well-known [...
Keyphrases
fitted hierarchical base multigrid convection-diffusion equation one-dimensional stationary convection-diffusion equation convectiondiffusion equation sobolev space homogeneous boundary condition gamma weakly differentiable function hierarchical base multigrid method key word finite element discretisation hierarchical base condition problem second derivative unique solution
