The convergence rate of approximate solutions for nonlinear scalar conservation laws. Final Report

Technical Report · Mon Jul 01 04:00:00 EDT 1991

OSTI ID:5071626

Nessyahu, HAIM; Tadmor, EITAN

The convergence rate is discussed of approximate solutions for the nonlinear scalar conservation law. The linear convergence theory is extended into a weak regime. The extension is based on the usual two ingredients of stability and consistency. On the one hand, the counterexamples show that one must strengthen the linearized L{sup 2}-stability requirement. It is assumed that the approximate solutions are Lip{sup +}-stable in the sense that they satisfy a one-sided Lipschitz condition, in agreement with Oleinik's E-condition for the entropy solution. On the other hand, the lack of smoothness requires to weaken the consistency requirement, which is measured in the Lip'-(semi)norm. It is proved for Lip{sup +}-stable approximate solutions, that their Lip'convergence rate to the entropy solution is of the same order as their Lip'-consistency. The Lip'-convergence rate is then converted into stronger L{sup p} convergence rate estimates.

• Research Organization: National Aeronautics and Space Administration, Hampton, VA (United States). Inst. for Computer Applications in Science and Engineering
• OSTI ID: 5071626
• Report Number(s): N-91-30866; NASA-CR--187608; NAS--1.26:187608; ICASE--91-62; CNN: NAS1-18605; N00014-91-J-1076
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
CONVERGENCE
DATA
DIFFERENTIAL EQUATIONS
ENTROPY
EQUATIONS
INFORMATION
NONLINEAR PROBLEMS
NUMERICAL DATA
NUMERICAL SOLUTION
PHYSICAL PROPERTIES
SCALARS
STABILITY
THEORETICAL DATA
THERMODYNAMIC PROPERTIES