Our main interest is in the numerical solution of partial differential equations using adaptive methods, particularly moving grid methods. The research focuses primarily on the following aspects and questions:
(i) determine which among the steady mesh generation systems is best suited to the development of moving mesh methods,
(ii) investigate various aspects of the numerical implementation,
(iii) develop finite element software based upon the moving mesh procedure,
(iv) use the software to solve difficult problems, partly in collaboration with engineers, and
(v) analyze properties such as stability, preservation of mesh qualities and potential mesh overlap.
Bob Russell