Volume 10, Issue 1
A New Post-Processing Technique for Finite Element Methods with $L^2$ -Superconvergence

Wei Pi ,  Hao Wang and Xiaoping Xie


East Asian J. Appl. Math., 10 (2020), pp. 40-56.

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  • Abstract

A simple post-processing technique for fifinite element methods with L2 -superconvergence is proposed. It provides more accurate approximations for solutions of twoand three-dimensional systems of partial differential equations. Approximate solutions can be constructed locally by using fifinite element approximations uh provided that uh is superconvergent for a locally defifined projection Phu. The construction is based on the least-squares fifitting algorithm and local L2 -projections. Error estimates are derived and numerical examples illustrate the effectiveness of this approach for fifinite element methods.

  • History

Published online: 2020-01

  • AMS Subject Headings

65N30, 65N15

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