Abstract
A generalized monotonicity theorem in the sense of Collatz is proved for almost linear elliptic boundary value problems of second order. This theorem is valid for continuous spline functions as used by the finite element method — in contrast to the classical theorems. The background is a generalized maximum principle with an interface condition for the normal derivatives which has been proven by Natterer/Werner in the case of the Laplace operator. Some numerical examples providing pointwise bounds for the solution of Dirichlet problems by cubic splines, the so called T 10 elements, are given.
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