A least squares finite element method applied to b-splines

In this article we construct a class of functions on a bounded irregular region Ω?R² which are of compact support, smooth and locally polynomials. The basic tool is the use of ordinary B-splines associated with the square containing Ω. This construction is then used for approximating the solution of Poisson's boundary value problem. The approximation is carried out through a least squares finite element method applied to the above class. Aside from some computational experiments, the objective is to emphasize the ease of generating the basis elements and the role of Kernel function in a convergence proof.