Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


A finite difference scheme for a system of two conservation laws with artificial viscosity

Author: David Hoff
Journal: Math. Comp. 33 (1979), 1171-1193
MSC: Primary 65N10
MathSciNet review: 537964
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we analyze an implicit finite difference scheme for the mixed initial-value Dirichlet problem for a system of two conservation laws with artificial viscosity. The system we consider is a model for isentropic flow in one space dimension. First, we show that, under certain conditions on the mesh, the scheme is stable in the sense that it possesses an invariant set (defined by the so-called Riemann invariants). We obtain this result as an extension of the same stability theorem for the Lax-Friedrichs scheme in the inviscid case. Second, we show that the approximants remain bounded and, in fact, decay to the boundary values as $ t \to \infty $. Finally, we obtain two $ O(\Delta {x^2})$ error bounds; the first grows exponentially in time while the second, which requires that the data have small oscillation, is independent of time.

References [Enhancements On Off] (What's this?)

  • [1] K. N. Chueh, C. C. Conley, and J. A. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Indiana Univ. Math. J. 26 (1977), no. 2, 373–392. MR 0430536 (55 #3541)
  • [2] YA. I. KANEL, "On some systems of quasilinear parabolic equations of the divergence type," U.S.S.R. Computational Math. and Math. Phys., v. 6, 1966, pp. 74-88.
  • [3] Peter Lax, Shock waves and entropy, Contributions to nonlinear functional analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971) Academic Press, New York, 1971, pp. 603–634. MR 0393870 (52 #14677)
  • [4] Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502 (28 #1725)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N10

Retrieve articles in all journals with MSC: 65N10

Additional Information

PII: S 0025-5718(1979)0537964-9
Article copyright: © Copyright 1979 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia