Spectral element method for elliptic equations with periodic boundary conditions

In this paper a nonconforming spectral element method is discussed for the elliptic partial differential equations with periodic boundary conditions. The formulation is based on the minimization of a functional by the least squares method. The periodic boundary conditions are added in the weak form in the formulation of the functional and the normal structure of resulting coefficient matrix is retained. To obtain the conforming solution a set of corrections are made and the error is estimated in H1 norm.