A local extrapolation method for hyperbolic conservation laws: the ENO and Goodman-LeVeque underlying schemes and sufficient conditions for TVD property

by Adongo, Donald Omedo

We start with linear single variable conservation laws and examine the conditions under

which a local extrapolation method (LEM) with upwinding underlying scheme is total

variation diminishing TVD. The results are then extended to non-linear conservation laws.

For this later case, we restrict ourselves to convex flux functions f, whose derivatives are

positive, that is, f? A0 and f? A0. We next show that the Goodman-LeVeque flux satisfies

the conditions for the LEM to be applied to it. We make heavy use of the CFL conditions,

the geometric properties of convex functions apart from the martingle type properties of

functions which are increasing, continuous, and differentiable.