An efficient discontinuous Galerkin method for advective transport in porous media

We consider a discontinuous Galerkin scheme for computing transport in heterogeneous media. An efficient solution of the resulting linear system of equations is possible by taking advantage of a priori knowledge of the direction of flow. By arranging the elements in a suitable sequence, one does not need to assemble the full system and may compute the solution in an element-by-element fashion. We demonstrate this procedure on boundary-value problems for tracer transport and time-of-flight.