ON A C++-PACKAGE FOR STUDYING THE BEHAVIOUR OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

of finite element methods allowing variational crimes. They can be applied
to elliptic boundary value problems, their main advantage being that they
yield highly accurate solutions which can be obtained by the fast, direct
linear solver 'nested dissection'. The statement of the final theorem was
predicted beforehand by extensive studies with a C++-Package developed for
this purpose. This process was simplified by the use of a simple script
interpreter wrapped around the C++ core algorithms. Since performance is
of great concern in numerical mathematics, special language constructs
were created to describe functions which are compiled into an
assembler-like pseudo-code internally, thus they are evaluated with great
speed while flexibility is retained. New features can be added to the
language easily, at present the author is working on a direct integration
of his 3D-Library for a more comfortable visualization of the results.
Inclusion of more advanced methods for the analysis of PDEs, like some
algorithms implemented at the University of Marburg for the computation of
solution branches to detect bifurcations, is also intended for the future.