## Convergence of difference schemes with high resolution for conservation laws

We are concerned with the convergence of Lax-Weridroff type schemes with high resolution to the entropy solutions fo: conservation laws. These schemes include the original Lax-Wendroff scheme proposed by Lax and Wendroff in 1960 and its two step versions-the Richtrayer scheme and the MacCormack scheme. For the convex scalar conservation laws with algebraic growth flux functions, we prove the convergence of these schemes to the weak solutions satisfying appropriate entropy inequalities. The proof is based on detailed Lp estimates of the approximate solutions, H-1 compactness estimates of the corresponding entropy dissipation measures, and some compensated compactness frameworks. Then these techniques are generalized to study the convergence problem for the nonconvex scalar case and the hyperbolic systems of conservation laws.

### Duke Scholars

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## Related Subject Headings

- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics

### Citation

*Mathematics of Computation*,

*66*(219), 1027–1053. https://doi.org/10.1090/s0025-5718-97-00859-4

*Mathematics of Computation*66, no. 219 (January 1, 1997): 1027–53. https://doi.org/10.1090/s0025-5718-97-00859-4.

*Mathematics of Computation*, vol. 66, no. 219, Jan. 1997, pp. 1027–53.

*Scopus*, doi:10.1090/s0025-5718-97-00859-4.

## Published In

## DOI

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics