Geodesic
A method of constructing 2D $4$-node and 3D $8$-node finite elements for solving elasticity problems
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 3, pp. 150-158

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A new method of constructing FEM schemes for solving 2D and 3D problems of continuum mechanics is proposed. The method is based on the projection of the rare mesh schemes of higher dimension linear finite elements on a 2D or 3D finite element mesh. Based on the example of a linear elasticity problem, the construction of 2D $4$-node and 3D $8$-node FEM schemes is considered. The obtained finite elements are similar to the known multilinear elements and are more efficient. The schemes contain parameters that make it possible to adjust the convergence of the numerical solutions. The possibility of applying this approach to the construction of numerical schemes for other problems of mathematical physics is shown.
Keywords: finite element method, rare mesh scheme, efficiency of numerical schemes, approximation, convergence of numerical solutions, elasticity theory. 
@article{UZKU_2013_155_3_a14,
     author = {D. T. Chekmarev},
     title = {A method of constructing {2D} $4$-node and {3D} $8$-node finite elements for solving elasticity problems},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {150--158},
     publisher = {mathdoc},
     volume = {155},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_3_a14/}
}
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D. T. Chekmarev. A method of constructing 2D $4$-node and 3D $8$-node finite elements for solving elasticity problems. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 3, pp. 150-158. http://geodesic.mathdoc.fr/item/UZKU_2013_155_3_a14/