Ober die Numerische Behandlung von Variationsproblemen mit Natorlichen Randbedingungen in Zwei Dimensionen

Abstract

We investigate the numerical solution of the nonlinear generalized Neumannproblem in a two dimensional rectangular region G. The boundary value problem is supposed to follow from a variational problem with natural boundary conditions,in which uniqueness of the solution u can only be obtained by imposing an additional condition, e.g. $\int\limits_G {u{\text{ }}dx} = 0{\text{ }}or{\text{ u(}}{{\text{x}}_0}{\text{) = 0}}$ for some ${x_0} \in \overline G$. Convergence is proven by means of an inequality relating certain norms of mesh functions.