Numerical Methods for Problems in Unbounded Domains
Weizhu Bao
Department of Mathematics
National University of Singapore
Many boundary value problems of partial differential equations (PDEs) involving unbounded domain occur in many areas of applications, e.g. fluid flow around obstacles, coupling of structures with foundation, wave propagation and radiation, quantum physics and chemistry etc. One of the main numerical difficulties is the unboundedness of physical domain.
In this talk, I first review different numerical approaches for problems in unbounded domain. Then I present high-order nonlocal/local artificial boundary conditions (ABCs) for second-order elliptic PDE and reduce it to a problem defined in a bounded computational domain. New `optimal' error estimates for the finite element approximation of the problem is reported. Extension of the results to Navier system for linear elastic and Stokes equations for incompressible material is given. Furthermore, the method is applied successfully to Navier-Stokes for incompressible viscous flow around obstacles. Numerical results are also reported to confirm our error estimates.