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 power-initial data. In this context we first recall Strang's theorem which shows that the classical Lax-Richtmyer 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 shock-discontinuities 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