A simple scheme for the finite element solution of a pure advection equation (Q1286836)

The paper deals with the finite element solution of an advection equation. The method of characteristic lines is combined with the finite element method, and three interpolating functions are employed: a cubic, a quadratic and a linear polynomial. The proposed scheme is also combined with a limiting procedure for suppression of numerical oscillations. The method is tested through four numerical examples: the advection of a box-shaped profile, the advection of an elliptic profile, the rotation of a cosine-shaped hill, and the advection of a square-shaped hill.