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Superconvergence of tetrahedral quadratic finite elements for a variable coefficient elliptic equation

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Abstract

For a variable coefficient elliptic boundary value problem in three dimensions, using the properties of the bubble function and the element cancelation technique, we derive the weak estimate of the first type for tetrahedral quadratic elements. In addition, the estimate for the W1,1-seminorm of the discrete derivative Green's function is also given. Finally, we show that the derivatives of the finite element solution uh and the corresponding interpolant Π2u are superclose in the pointwise sense of the L-norm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

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