A Total Variation Diminishing-Projection Method for Solving Implicit Numerical Schemes for Scalar Conservation Laws
The stability of Newton's method applied to implicit numerical schemes for scalar conservation laws requires, in the general case, an upper bound on the size of the timesteps. A simple locally defined projection, a total variation diminishing (TVD)-projection, is introduced, and it is used to obtain always-stable extensions of Newton's method. A numerical study of this method applied to Godunov's implicit scheme is presented.
A brief overview is presented of the VAMAS Surface Chemical Analysis Technical Working Party project. This project is aimed at providing the reference working base for surface analysis. There are currently 20 projects covering AES, XPS, SIMS, sputtered neutral mass spectrometry and sputter-depth profiling. The coordination of the projects leads to considerable gains in confidence and in project output, together with a reduction in the workload necessary to meet the project targets. This arises simply because of the increased availability of characterized samples, reference methodologies and software within the overall programme. This Technical Working Party has been active for 4 years now and definitive milestones are being achieved that would be impossible without the overall coordination.