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A new quadratic nonconforming finite element on rectangles

✍ Scribed by Heejeong Lee; Dongwoo Sheen

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
182 KB
Volume
22
Category
Article
ISSN
0749-159X

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✦ Synopsis

A new quadratic nonconforming finite element on rectangles (or parallelograms) is introduced. The nonconforming element consists of P 2 βŠ• Span{x 2 y, xy 2 } on a rectangle and eight degrees of freedom. Our element is essentially of seven degrees of freedom since the degree of freedom associated with the integration on rectangle is essentially of bubble-function nature. Global basis functions are constructed for both Dirichlet and Neumann type of problems; accordingly the corresponding dimensions are counted. The local and global interpolation operators are defined. Error estimates of optimal order are derived in both broken energy and L 2 ( ) norms for second-order of elliptic problems. Brief numerical results are also shown to confirm the optimality of the presented quadratic nonconforming element.

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