ERROR-ESTIMATES FOR THE APPROXIMATE SOLUTIONS OF A NONLINEAR HYPERBOLIC EQUATION GIVEN BY FINITE-VOLUME SCHEMES

This paper is devoted to the study of an error estimate of the finite volume approximation to the solution u is an element of L-infinity (R- N x R) of the equation u(t) + div(vf(u)) = 0, where v is a vector func tion depending on time and space. A 'h(1/4)' error estimate for an ini tial value in BV(R-N) is shown for a large variety of finite volume mo notonous flux schemes, with an explicit or implicit time discretizatio n. For this purpose, the error estimate is given for the general setti ng of approximate entropy solutions, where the error is expressed in t erms of measures in R-N and R-N x R. The study of the implicit schemes involves the study of the existence and uniqueness of the approximate solution. The cases where an 'h(1/2)' error estimate can be achieved are also discussed.