In this paper, radial basis functions that are compactly supported and give rise to positive definite interpolation matrices for scattered data are discussed. They are related to the well-known thin plate spline radial functions which are highly useful in applications for gridfree approximation methods. Also, encouraging approximation results for the compactly supported radial functions are shown.

We analyze multiscale Galerkin methods for strongly elliptic boundary integral equations of order zero on closed surfaces in $R^3$. Piecewise polynomial, discontinuous multiwavelet bases of any polynomial degree are constructed explicitly. We show that optimal convergence rates in the boundary energy norm and in certain negative norms can be achieved with "compressed" stiffness matrices containing $O(N({\log N})^2)$ nonvanishing entries ...

In many technical applications it is necessary to compute a numerical solution of complex flow problems in several space dimensions. Most available codes split the multi-dimensional problem into several one-dimension\-al ones. Those are aligned with the cell interfaces of the underlying grid. In some of the applications, e.g.high Mach number flow, this approach does not work very well, since the physical properties of the model equations ...