An adaptive discontinuous finite element method for the transport equation (Q1346553)

The authors discuss a discontinuous finite element method for the transport equation. Because of its local nature, the solution is allowed to be discontinuous across the interelement boundaries and this provides a basis for an adaptive procedure. The proposed scheme combines the nice features of the finite element method with non-oscillating finite difference procedures. The method is of arbitrary order and can be applied in an explicit manner on quite irregular grids. Moreover, it provides with two different error indicators. The first one uses the dual problem in a standard way, while the second one is based on increasing the degree of the approximating polynomials. In fact the later error indicator is able to tackle arbitrary varying flow directions. Finally, some numerical experiments are presented to demonstrate the performance of the scheme.