Geodesic
Comparison of the scalar and vector form FEM for example elliptic cylinders
Matematičeskoe modelirovanie, Tome 28 (2016) no. 1, pp. 65-77

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The algorithm of forming the stiffness matrix curvilinear quadrilateral finite element as a fragment of the middle surface of an elliptic cylinder with eighteen degrees of freedom in the node is presented. When implementing a finite-element procedure two versions of approximation of the unknown quantities are implemented: scalar and vector. Numerical examples proved that the vector approximation had fundamental advantages compared with the scalar approximation in the calculation of arbitrary shells with significant gradients of curvature of the middle surface or allowing the displacement as a rigid body.
Keywords: approximation vector, scalar approximation, finite element, elliptic cylinder, displacement as a rigid body shell. 
@article{MM_2016_28_1_a4,
     author = {Yu. V. Klochkov and A. P. Nikolaev and T. A. Kiseleva},
     title = {Comparison of the scalar and vector form {FEM} for example elliptic cylinders},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {65--77},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_1_a4/}
}
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Yu. V. Klochkov; A. P. Nikolaev; T. A. Kiseleva. Comparison of the scalar and vector form FEM for example elliptic cylinders. Matematičeskoe modelirovanie, Tome 28 (2016) no. 1, pp. 65-77. http://geodesic.mathdoc.fr/item/MM_2016_28_1_a4/