Error Estimate for the Finite Volume Approximate of the Solution to a Nonlinear Convective Equation

This paper is mainly concerned with the study of an error estimate of the finite volume approximation to the solution u L (ℝN X ℝ) of the equation u _t +div(vf(u)) = 0, where v is a vector function depending on time and space. A “h1/4” error estimate for an initial value in BV(ℝN) is shown for a large variety of finite volume monotoneous flux schemes, with an explicit or implicit time discretization. For this purpose, the error estimate is given for the general setting of solutions of approximate continuous entropy solutions, where the error is expressed in terms of measures in ℝN X ℝ. All the proofs of this paper can be found in [7].