On finite element methods for the Neumann problem

Summary The Neumann problem for a second order elliptic equation with self-adjoint operator is considered, the unique solution of which is determined from projection onto unity. Two variational formulations of this problem are studied, which have a unique solution in the whole space. Discretization is done via the finite element method based on the Ritz process, and it is proved that the discrete solutions converge to one of the solutions of the continuous problem. Comparison of the two methods is done.