Errors and optimality for spatial approximations in one-dimensional transport

Abstract

In this paper, we apply a recently developed branch of theoretical computer science, information-based complexity, to numerical transport theory. Two classes of information, cell-average information and point-evaluation information, and two popular algorithms, step characteristics and diamond differences, are discussed in view of information-based complexity, for a one-dimensional model problem. For this problem, we show that the diamond difference method always has a smaller worst-case error than the step-characteristic method, when both use the same cell-average information. Optimal methods for these two types of information also are presented.