Communications in Mathematical Sciences
Volume 6 (2008)
Stability of reconstruction schemes for scalar hyperbolic conservations laws
Pages: 57 – 70
We study the numerical approximation of scalar conservation laws in dimension 1 via general reconstruction schemes within the finite volume framework. We exhibit a new stability condition, derived from an analysis of the spatial convolutions of entropy solutions with characteristic functions of intervals. We then propose a criterion that ensures the existence of some numerical entropy fluxes. The consequence is the convergence of the approximate solution to the unique entropy solution of the considered equation.
hyperbolic equations, numerical schemes, reconstruction schemes, entropy schemes
2010 Mathematics Subject Classification
Published 1 January 2008