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