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A nonconforming mixed finite element for second-order elliptic problems

โœ Scribed by Mohamed Farhloul; And Michel Fortin

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
131 KB
Volume
13
Category
Article
ISSN
0749-159X

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โœฆ Synopsis

In a recent work, Hiptmair [Mathematisches Institut, M9404, 1994] has constructed and analyzed a family of nonconforming mixed finite elements for second-order elliptic problems. However, his analysis does not work on the lowest order elements. In this article, we show that it is possible to construct a nonconforming mixed finite element for the lowest order case. We prove the convergence and give estimates of optimal order for this finite element. Our proof is based on the use of the properties of the so-called nonconforming bubble function to control the consistency terms introduced by the nonconforming approximation. We further establish an equivalence between this mixed finite element and the nonconforming piecewise quadratic finite element of Fortin and Soulie [

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