Approximation properties of the Generalized Finite Element Method |
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Authors: | C Anitescu U Banerjee |
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Institution: | (1) Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA;(2) Department of Mathematics, Kangwon National University, Chunchon, 200-701, South Korea |
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Abstract: | In this paper, we have obtained an approximation result in the Generalized Finite Element Method (GFEM) that reflects the
global approximation property of the Partition of Unity (PU) as well as the approximability of the local approximation spaces.
We have considered a GFEM, where the underlying PU functions reproduce polynomials of degree l. With the space of polynomials of degree k serving as the local approximation spaces of the GFEM, we have shown, in particular, that the energy norm of the GFEM approximation
error of a smooth function is O(h
l + k
). This result cannot be obtained from the classical approximation result of GFEM, which does not reflect the global approximation
property of the PU. |
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Keywords: | |
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