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- gr...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.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11271035 and 11031006)
文摘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.
