L∞- and L2-norms superconvergence of the tetrahedral quadratic finite element.

Consider the quadratic finite element method over a regular family of uniform tetrahedral partitions for the three-dimensional Poisson equation. Utilizing properties of the bubble function and estimates for discrete Green's function, we derive a pointwise superconvergent estimate for the finite element approximation in the sense of L ∞ -norm. Furthermore, the L 2 -norm superconvergent estimate is also provided. A numerical example is presented to demonstrate the accuracy of the theoretical results. [ABSTRACT FROM AUTHOR]