
Accession Number : ADA240684
Title : The Convergence Rate of Approximate Solutions for Nonlinear Scalar Conservation Laws.
Descriptive Note : Final rept.,
Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
Personal Author(s) : Nessyahu, Haim ; Tadmor, Eitan
Report Date : JUL 1991
Pagination or Media Count : 22
Abstract : We are concerned here with the convergence rate of approximate solutions for the nonlinear scalar conservation law, u sub t + f sub x (u) + 0 with C sub o to the 1st powerinitial data. In this context we first recall Strang's theorem which shows that the classical LaxRichtmyer linear convergence theory applies for such nonlinear problem, as long as the underlying solution is sufficiently smooth. Since the solutions of the nonlinear conservation law develop spontaneous shockdiscontinuities at a finite time, Strang's result does not apply beyond this critical time. Indeed, the Fourier method as well as other L squared  conservative schemes provide simple counterexamples of a consistent approximations which fail to converge (to the discontinuous entropy solution), despite their linearized L squared  stability. In this paper we extend the linear convergence theory into the weak regime. The extension is based on the usual two ingredients of stability and consistency.
Descriptors : APPROXIMATION(MATHEMATICS), CONSERVATION, CONSISTENCY, CONVERGENCE, ENTROPY, FOURIER ANALYSIS, LINEARITY, LOW STRENGTH, NONLINEAR SYSTEMS, RATES, RECALL, SCALAR FUNCTIONS, SOLUTIONS(GENERAL), STABILITY, THEORY, TIME.
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE