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Composite mixed finite elements on plane quadrilaterals
Author(s) -
Bendali A.,
Lahmar N.
Publication year - 1993
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690090505
Subject(s) - quadrilateral , mathematics , finite element method , mixed finite element method , interpolation (computer graphics) , affine transformation , degrees of freedom (physics and chemistry) , plane (geometry) , integer (computer science) , regular polygon , space (punctuation) , geometry , mathematical analysis , pure mathematics , structural engineering , physics , engineering , motion (physics) , linguistics , philosophy , classical mechanics , quantum mechanics , computer science , programming language
Mixed finite elements over a plane convex quadrilateral are obtained by assembling two Raviart‐Thomas mixed finite elements over triangles. The macroelement is given by an eliminating procedure of the degrees of freedom related to the common edge to the two triangles. This procedure results in a finite element with a space of interpolating functions containing the polynomials of degree ⩽ l , where l is the greater integer for which the same property is satisfied by the relevant Raviart‐Thomas [ Mathematical Aspects of Finite Element Methods, Roma 1975 , I. Galligani and E. Magenes, Eds., Lecture Notes in Mathematics Vol. 606, Springer‐Verlag, Berlin, 1975] mixed finite element. The interpolation error is estimated by means of the technique of almost equivalent affine element as given by Ciavaldini and Nédélec [ Rev. Fr. Autom. Inf. Recher. Opérationnelle Ser. Rouge R2 , 29–45 (1974)]. © 1993 John Wiley & Sons, Inc.