Shortly after this the use of Bernstein polynomials and then B-splines was introduced into surface representation mathematics, and a lot is now known about these bases.
Back of envelope calculations indicate that for solid elliptic problems there should be a saving of a factor of four in number of degrees of freedom and a factor of three on bandwidth for direct solution (and probably a factor of four on condition number) if a B-spline basis is used instead of the current serendipity elements.
The first part of the project is to elaborate on this saving, and demonstrate it by prototype software.
The second part is to find out how to maintain the topological freedom of the finite element method, so that realistically complex objects may be analysed.
(Malcolm Sabin email:-email@example.com)