On the Convergence of Fully-discrete High-Resolution Schemes with van Leer's Flux Limiter for Conservation Laws

• Autores: Nan Jiang
• Localización: Methods and applications of analysis, ISSN 1073-2772, Vol. 16, Nº 3, 2009, págs. 403-422
• Idioma: inglés
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• Resumen

  • A class of fully-discrete high-resolution schemes using flux limiters was constructed by P. K. Sweby [SIAM J. Numer. Anal. 21 (1984), 995-1011], which amounted to add a limited anti-diffusive flux to a first order scheme. This technique has been very successful in obtaining high-resolution, second order, oscillation free, explicit difference schemes. However, the entropy convergence of such schemes has been open. For the scalar convex conservation laws, we use one of Yang's convergence criteria [SIAM. J. Numer. Anal. 36 (1999) No. 1, 1-31] to show the entropy convergence of the schemes with van Leer's flux limiter when the building block of the schemes is the Godunov or the Engquish-Osher. The entropy convergence of the corresponding problems in semi-discrete case, for convex conservation laws with or without a source term, has been settled by Jiang and Yang [Methods and Applications of Analysis 12 (2005), No. 1, 089-102].