Title: Least-Squares Finite Element Methods.

Abstract.

It is well-known that the standard Galerkin method produces a unique
approximating solution with the restriction of small meshsize when there
is a unique solution for the continuous problem.  On the other hand, it is
easy to construct an example such that the standard Galerkin method fails
to produce a unique solution.

In this talk, I will present two least-squares methods which guarantee the
existence and the uniqueness of the approximating solution without the
restriction of small meshsize.  Various error estimates with confirming
numerics will be provided.