Abstract
For a variable coefficient elliptic boundary value problem in three dimensions, using the properties of the interpolation operator of projection type, we derive the weak estimate of the first type for the quadratic serendipity block finite element. In addition, the estimate for the W1,1 -seminorm of the discrete derivative Green's function is given. Finally, we prove that the derivatives of the finite element approximation and the corresponding interpolant of projection type are superclose in the pointwise sense of the L∞ -norm. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1253-1261, 2011
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