On finite element methods for the Neumann problem (Q1061468)

This paper is concerned with the finite element approximation of the Neumann problem for a second order equation with self-adjoint operator, the unique solution of which is determined from projection onto unity. The domain \(\Omega\) is a bidimensional polygon. Two minimization problems, one over \(H^ 1(\Omega)\) and the otherone over a subset of it, are considered. They represent variational formulations of the original problem; hence the finite element technique is based on the Ritz method. Convergence results including the order of convergence are given. The influence of errors in the right-hand side and in the boundary conditions on the solution is treated. The two given methods are compared concerning their possible numerical implementation; no numerical results are given.