INTERIOR ESTIMATES FOR NONCONFORMING FINITE-ELEMENT METHODS

Interior error estimates are derived for a wide class of nonconforming finite element methods for second order scalar elliptic boundary valu e problems. It is shown that the error in an interior domain can be es timated by three terms: the first one measures the local approximabili ty of the finite element space to the exact solution, the second one m easures the degree of continuity of the finite element space (the cons istency error), and the last one expresses the global effect through t he error in an arbitrarily weak Sobolev norm over a slightly larger do main. As an application, interior superconvergences of some difference quotients of the finite element solution are obtained for the derivat ives of the exact solution when the mesh satisfies some translation in variant condition.