This document discusses accuracy of the collocation technique we employ to calculate the velocity field in ambient inviscid fluid above an interface swollen by a denser source fluid.

Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations (RPIEs). We outline how Fourier and Laplace transforms can be used to obtain an O(h) convergence result for a “polar” piecewise–linear collocation approximation of a scalar RPIE on an infinite flat plate.

Abstract: Condition numbers for infinite-dimensional optimization, as defined in Zolezzi (2002, 2003), are shown to exhibit a stable behavior when employing finite-dimensional solution methods of the Ritz type, in particular finite elements. The same behavior is shown to hold in connection with the so called extended Ritz method.

Eigenvalue estimates that are optimal in some sense have selfevident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating matrix eigenvalues that are situated well into the interior of the spectrum revisit from time to time methods that are known to yield optimal bounds. This artic...

This paper considers the finite element approximation of elliptic boundary value problems in divergence form with rough coefficients. The solution of such problems will, in general, be rough, and it is well known that the usual (Ritz or displacement) finite element method will be inaccurate in general. The purpose of the paper is to help clarify the issue of whether the use of mixed variational...

An alternative to the classical Ritz method for approximate optimization is investigated. In the extended Ritz method, sets of admissible solutions are approximated by their intersections with sets of linear combinations of all n-tuples of functions from a given basis. This alternative scheme, called variable-basis approximation, includes functions computable by trigonometric polynomials with f...