Error estimate for the approximation of nonlinear conservation

Error estimate for the approximation of nonlinear conservation laws on bounded domains by the nite volume method Mario Ohlberger Julien Vovelle y Abstract In this paper we derive a priori and a posteriori error estimates for cell centered nite volume ap proximations of nonlinear conservation laws on polygonal bounded domains Numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies Keywords hyperbolic equation initialboundary value problem nite volume method error estimate MSC LN Introduction Let be an open convex polygonal bounded domain in IR d d endowed with the Euclidean norm j j and let T IR We consider the following initial boundary value problem for nonlinear scalar conservation laws c t r F x t c in T c c in c x t c t x in T The ux in equation is given by the function F C T IR IR d the functions c L and c L T are respectively the initial and boundary data of the problem The nite volume methods are known to be wellsuited for the discretization of conservation laws A basic account for this claim is the fact that by construction they respect the conservation principle which constitutes the root of equation Indeed the evolution of the discrete unknown c K in each control volume K is given by the equation jKj c n K jKj c n K t n X K Q n

• volume method


• numerical ux


• entropy solution


• cauchy problem


• volume method let


• error estimates


• ghost control


• nite volume