Multi-Component Schemes

Overview

The subject of Chapter 7 has been the separation and investigation of the diverse error sources that act on the approximation quality in case of the Van Kan scheme (with β ≥ 1/2). Especially, we treated the consistency error independently of those errors that stem from the quasi-compressibility constraint. Finally, we dealt with the particular problems that arise in the case of incompatibly posed initial data, both, from the theoretical and the computational point of view. As a result, we furnished that the assumptions given in Postulate B ₂ are necessary to secure a second order convergence rate, otherwise there might be a global reduction of order of convergence for the approximation ũ ^m+l from O(k ²log1/k) to O(k).