Approximation properties of the Generalized Finite Element Method

Authors:
C. Anitescu;U. Banerjee
Affiliations:
Department of Mathematics, Syracuse University, Syracuse, USA 13244;Department of Mathematics, Syracuse University, Syracuse, USA 13244
Venue:
Advances in Computational Mathematics
Year:
2011

Citing 2
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Special finite element methods for a class of second order elliptic problems with rough coefficients

SIAM Journal on Numerical Analysis
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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驴+驴k ). This result cannot be obtained from the classical approximation result of GFEM, which does not reflect the global approximation property of the PU.