Variable-order finite elements and positivity preservation for hyperbolic PDEs Original Research Article

A family of positivity-preserving finite element methods are considered for the solution of the advection equation in one space dimension. The approach uses B-spline spatial discretization methods in conjunction with forward Euler timestepping and a mass matrix iteration that preserves positivity. The method is compared against a positivity-preserving finite volume scheme on travelling wave and pulse examples including an inviscid Burgersʹ equation example.