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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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Springer Berlin Heidelberg

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DOI

10.1002/pssb.2221040227

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1869-1862

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Nonconforming finite element methods on quadrilate

Authors: Jun Hu ShangYou Zhang
Publish Date: 2013/10/16
Volume: 56, Issue: 12, Pages: 2599-2614
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Abstract

It is well known that it is comparatively difficult to design nonconforming finite elements on quadrilateral meshes by using GaussLegendre points on each edge of triangulations One reason lies in that these degrees of freedom associated with these GaussLegendre points are not all linearly independent for usual expected polynomial spaces which explains why only several lower order nonconforming quadrilateral finite elements can be found in literature The present paper proposes two families of nonconforming finite elements of any odd order and one family of nonconforming finite elements of any even order on quadrilateral meshes Degrees of freedom are given for these elements which are proved to be welldefined for their corresponding shape function spaces in a unifying way These elements generalize three lower order nonconforming finite elements on quadrilaterals to any order In addition these nonconforming finite element spaces are shown to be full spaces which is somehow not discussed for nonconforming finite elements in literature before

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