The Mathematical Institute, University of Oxford, Eprints Archive

Diagonal Dominance and Positive Definiteness of Upwind Approximations for Advection Diffusion Problems

Golub, Gene H. and Silvester, David and Wathen, A. J. (1996) Diagonal Dominance and Positive Definiteness of Upwind Approximations for Advection Diffusion Problems. Technical Report. Unspecified. (Submitted)

[img]
Preview
PDF
140Kb

Abstract

We examine whether three different upwind schemes for the positive definite advection diffusion problem can yield indefinite coefficient matrices. In particular, in line with the increasing use of adaptive meshes, we are concerned with discretisations on arbitrary grids but only in one dimension. We show that indefinite coefficient matrices can arise from certain approaches: this can present difficulties with efficient iterative solution techniques which might be required for corresponding approximations in higher dimensions.

We dedicate this paper to Professor Ron Mitchell who has been an inspiration to many generations of numerical analysts. In addition his generous spirit has infused our discipline with a sense of positive endeavour.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1331
Deposited By:Lotti Ekert
Deposited On:12 Jun 2011 09:53
Last Modified:12 Jun 2011 09:53

Repository Staff Only: item control page