Nonconforming finite element methods on quadrilateral meshes  

作　　者：HU Jun ZHANG ShangYou 

机构地区：[1]LMAM and School of Mathematical Sciences, Peking University [2]Department of Mathematical Sciences, University of Delaware,Newark, DE 19716, USA

出　　处：《Science China Mathematics》2013年第12期2599-2614,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11271035 and 11031006)

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

关 键 词：nonconforming finite element RECTANGLE 

分 类 号：O241.82[理学—计算数学] TP391.72[理学—数学]