Asymptotic Expansion and Superconvergence for Triangular Linear Finite Element on a Class of Typical Mesh
Year: 2012
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 4 : pp. 892–906
Abstract
In this paper, we present a new approach to obtain the asymptotic expansion and superconvergence for the linear element on Union Jack mesh. First, we construct a generalized interpolation function and its discrete harmonic extension by using the energy embedding method and the method of separation of variables. Then, we present elaborate estimates for the generalized interpolation function and the harmonic extension. Finally, the asymptotic expansion, superconvergence and extrapolation are obtained based on those estimates.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-664
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 4 : pp. 892–906
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Finite element Superconvergence Asymptotic expansion Extrapolation Discrete harmonic extension.