Second-order finite-volume schemes for a non-linear hyperbolic equation: Error estimate

We study second-order finite-volume schemes for the non-linear hyperbolic e quation u(t)(x,t) + div F(x, t, u(x, t)) = 0 with initial condition u(0). T he main result is the error estimate between the approximate solution given by the scheme and the entropy solution. It is based on some stability prop erties verified by the scheme and on a discrete entropy inequality. If u(0) is an element of L-infinity boolean AND BV1 infinity(R-N), we get an error estimate of order h(1/4), where h defines the size of the mesh. Copyright (C) 2000 John Wiley & Sons, Ltd.