Analysis of the advection-diffusion operator using fractional order norms

Authors:
Giancarlo Sangalli
Affiliations:
Istituto di Matematica Applicata e Tecnologie Informatiche del C.N.R., Italia
Venue:
Numerische Mathematik
Year:
2004

Citing 0
Cited 2

Stability of a streamline diffusion finite element method for turning point problems

Journal of Computational and Applied Mathematics
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we obtain a family of optimal estimates for the linear advection-diffusion operator. More precisely we define norms on the domain of the operator, and norms on its image, such that it behaves as an isomorphism: it stays bounded as well as its inverse does, uniformly with respect to the diffusion parameter. The analysis makes use of the interpolation theory between function spaces. One motivation of the present work is our interest in the theoretical properties of stable numerical methods for this kind of problem: we will only give some hints here and we will take a deeper look in a further paper.