A local extrapolation method for hyperbolic conservation laws: the ENO and Goodman-LeVeque underlying schemes and sufficient conditions for TVD property
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.
School:Kansas State University
School Location:USA - Kansas
Source Type:Master's Thesis
Keywords:conservation laws tvd eno extrapolation mathematics 0405
Date of Publication:01/01/2008