EULER CHARACTERISTIC GALERKIN SCHEME WITH RECOVERY

This paper describes a general formulation of the Euler Characteristic Galerkin (ECG) scheme for scalar conservation laws, based on the theo ry of the Riemann-Stieltjes integral. The ECG scheme is proved to be e quivalent to the projection of Brenier's transport-collapse operator. For the purpose of getting higher order accuracy, we explore two recov ery procedures, namely continuous linear recovery and discontinuous li near recovery. Some estimates are obtained for proving the convergence of the ECG scheme. Finally we prove that the limit Junction of the ap proximation constructed by the ECG scheme with recovery is an admissib le solution of the conservation law.