Abstract. The regularity or smoothness of a domain surface has often been noted to have a varying effect on the solution of partial differential equations (PDEs). In this talk I shall examine the use of subdivision surfaces as adaptive and higher-order finite elements for two different PDEs: an anistropic geometric diffusion model for surface and function on surface noise removal, and an Helmholtz equation for acoustics scattering for use in designing hearing aids. Several experimental results as well as open problems shall also be presented.

This is joint work with Professor Guoliang Xu of State Key Lab in Scientific Computation, Chinese Academy of Sciences, Beijing.