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Abstract
The main theme of my thesis is numerical solution of partial differential equations using a least squares finite element method. As a first step, a class of functions with sufficient smoothness properties on an irregular region is being constructed. This class is then used as an approximating basis for a finite element technique. The model problem being considered is the Poisson's equation on a bounded region. With the aide of kernel functions from potential theory, the pointwise convergence of our approximation is established. The method is then applied to the Biharmonic equation. Finally the so called Navier's equation is being considered. This is a coupled system of linear elliptic equations which arises naturally in elasticity theory. The close connection between potential theory and the theory of elasticity allows us to prove pointwise convergence in the case of this elliptic system. Several numerical examples are considered which support the theoretical aspects of the thesis.
