Mixed finite element methods for general quadrilateral grids

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We study a new mixed finite element of lowest order for general quadrilateral grids which gives optimal order error in the H(div)-norm. This new element is designed so that the H(div)-projection Pi(h) satisfies del . Pi(h) = P(h)div. A rigorous optimal order error estimate is carried out by proving a modified version of the Bramble-Hilbert lemma for vector variables. We show that a local H(div)-projection reproducing certain polynomials suffices to yield an optimal L(2)-error estimate for the velocity and hence our approach also provides an improved error estimate for original Raviart-Thomas element of lowest order. Numerical experiments are presented to verify our theory. (C) 2011 Elsevier Inc. All rights reserved.
Publisher
ELSEVIER SCIENCE INC
Issue Date
2011-03
Language
English
Article Type
Article
Citation

APPLIED MATHEMATICS AND COMPUTATION, v.217, no.14, pp.6556 - 6565

ISSN
0096-3003
DOI
10.1016/j.amc.2011.01.036
URI
http://hdl.handle.net/10203/98730
Appears in Collection
MA-Journal Papers(저널논문)
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