SINOPSIS

A standard h-adaptive finite element procedure based on a-posteriori error-estimation is described. The pure advection equation is solved (in both steady and transient states) using the SUPG (streamline upwind Petrov-Galerkin) form of the finite element method. Applied to standard benchmark problems (of uniform flow advecting discontinuous functions) the SUPG method on its own is insufficient to resolve the sharp discontinuities present when used with a uniform mesh. Although the solution is a significant improvement on other methods, it still suffers with sharp overshoots and undershoots on either side of the discontinuity. The well-known plague of numerical models of advection, false diffusion, is also evident. When an h-adaptive procedure is used in combination with the SUPG formulation (with a discontinuity capturing term), high quality solutions are obtained for both the steady and transient benchmark problems.