THE POSITIVE AND NEARLY CONSERVATIVE LAGRANGE-GALERKIN METHOD

The Lagrange-Galerkin method has proved very successful, but it has problems with positivity and conservation. In this paper we address these two issues and propose an algorithm that allows no new extrema to be generated by the scheme. It is equally applicable to multi-dimensions, and also prevents the creation of any systematic error in conserved quantities. Furthermore this is achieved at very little additional cost and without compromising the unconditional stability of the method.