5. EXACT SOLUTIONS
Circle, annulus, sectors
Rectangle, certain triangles, ellipse
SEMI-ANALYTIC METHODS
Boundary perturbation
Domain decomposition
Internal matching
Variational
Asymptotic
Point match
Galerkin
Conformal map
Green’s function
Boundary integral

7. Boundary Perturbation

10. Domain decomposition

12. Internal matching

24. Discussions
A) The best method to use depends on the problem
B) With FD FE codes, why study analytic or semi-analytic methods?
Analytic methods serve as a check for numerical codes which are better in more complicated situations
Sharp edges, point constraints are difficult to handle for full numerical codes
These methods can be applied to other elliptic pde’s such as Stokes flow.