Convergence rate of Godunov type schemes

Haim Nessyahu, Eitan Tadmor, Tamir Tassa

Research output: Contribution to journalArticlepeer-review


Godunov type schemes form a special class of transport projection methods for the approximate solution of nonlinear hyperbolic conservation laws. The authors study the convergence rate of such schemes in the context of scalar conservation laws and show how the question of consistency for Godunov type schemes can be answered solely in terms of the behavior of the associated projection operator. Namely, they prove that Lip′-consistent projections guarantee the Lip′-convergence of the corresponding Godunov scheme, provided the latter is Lip+-stable. This Lip′-error estimate is then translated into the standard Ws,p global error estimates (-1 ≤ s ≤ 1÷p, 1 ≤ p ≤ ∞) and finally to a local Lloc convergence rate estimate. These convergence rate estimates are applied to a variety of scalar Godunov type schemes on a uniform grid as well as variable mesh size ones.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalSIAM Journal on Numerical Analysis
Issue number1
StatePublished - 1994
Externally publishedYes


Dive into the research topics of 'Convergence rate of Godunov type schemes'. Together they form a unique fingerprint.

Cite this