CONVERGENCE AND ERROR-ESTIMATES IN FINITE-VOLUME SCHEMES FOR GENERAL MULTIDIMENSIONAL SCALAR CONSERVATION-LAWS .1. EXPLICIT MONOTONE SCHEMES

Authors
VILA JP
Citation
Jp. Vila, CONVERGENCE AND ERROR-ESTIMATES IN FINITE-VOLUME SCHEMES FOR GENERAL MULTIDIMENSIONAL SCALAR CONSERVATION-LAWS .1. EXPLICIT MONOTONE SCHEMES, Modelisation mathematique et analyse numerique, 28(3), 1994, pp. 267-295
Citations number
18
Categorie Soggetti
Mathematics,Mathematics
Journal title
Modelisation mathematique et analyse numerique → ACNP
ISSN journal
0764583X
Volume
28
Issue
3
Year of publication
1994
Pages
267 - 295
Database
ISI
SICI code
0764-583X(1994)28:3<267:CAEIFS>2.0.ZU;2-T
Abstract
We study here the convergence of Finite Volume schemes of monotone typ e for general multidimensional conservation laws. By generalizing a pr evious result of Kuznetsov for Finite Difference schemes, we obtain un der general assumptions error bounds in h1/4 when the initial conditio n lies in BV(R(d)); convergence follows for initial conditions in L(in finity)(R(d)) and L1(R(d)).