Title:
A General Algorithm for  Variable Order Finite Element and Positivity
Preservation for Hyperbolic PDEs

Absract:
An h-p family of positivity finite elements methods is derived for the
solution of the advection equations in one or two space dimensions .
The approach uses spatial discretisation methods in which the order is
varied within a constrained approximation space in conjunction with
a timestepping and a mass matrix iteration that preserves positivity.
The approach is a timestepping and a mass matrix iteration that preserves
positivity. The approach is extended to the solution of systems of
conservation laws in one space dimension and two dimensional problems. The
effectiveness of the approach is demonstrated through computational
examples.