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In this paper, we present a simple adaptive finite element method for second order elliptic partial differential equations, which is a modification of the MNS algorithm of  and  by Morin, Nochetto and Siebert.
A simple adaptive finite element method. We start this section with some useful notation.
We say that an adaptive finite element method realizes optimal convergence rates if whenever (u, f) [member of] [W.sup.s], it produces the approximation [u.sub.k] with respect to the triangulation [T.sub.k] such that
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