Higher order local accuracy by averaging in the finite element method

This chapter describes the class of finite element subspaces and explains the main result on the accuracy of K h * u h ,where K h is a fixed function, u h represents local averages, and * denotes convolution. The function K h has the following properties: (1) K h has small support; (2) K h is independent of the specific choice of S h or the operator L; (3) K h * u h is easily computable from u h ; and (4) K h * u h approximates u to higher order than does u h . The chapter also discusses on notation, subspaces and the construction of K h .

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