The Triangular Hermite Finite Element Complementing the Bogner-Fox-Schmit Rectangle

Affiliation(s)

Institute of Computational Modeling, Siberian Branch of Russian Academy of Sciences, Krasnoyarsk, Russia.

Institute of Computational Modeling, Siberian Branch of Russian Academy of Sciences, Krasnoyarsk, Russia;Vladimir Shaydurov.

Siberian Federal University, Krasnoyarsk, Russia.

Institute of Computational Modeling, Siberian Branch of Russian Academy of Sciences, Krasnoyarsk, Russia.

Institute of Computational Modeling, Siberian Branch of Russian Academy of Sciences, Krasnoyarsk, Russia;Vladimir Shaydurov.

Siberian Federal University, Krasnoyarsk, Russia.

Abstract

The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied only on a simple domain composed of rectangles or parallelograms whose sides are parallel to two different straight lines. We propose a new triangular Hermite element with 13 degrees of freedom. It is used in combination with the Bogner-Fox-Schmit element near the boundary of an arbitrary polygonal domain and provides continuous differentiability of an approximate solution in the whole domain up to the boundary.

Keywords

Continuously Differentiable Finite Elements; Bogner-Fox-Schmit Rectangle; Triangular Hermite Element

Continuously Differentiable Finite Elements; Bogner-Fox-Schmit Rectangle; Triangular Hermite Element

Cite this paper

L. Gileva, V. Shaydurov and B. Dobronets, "The Triangular Hermite Finite Element Complementing the Bogner-Fox-Schmit Rectangle,"*Applied Mathematics*, Vol. 4 No. 12, 2013, pp. 50-56. doi: 10.4236/am.2013.412A006.

L. Gileva, V. Shaydurov and B. Dobronets, "The Triangular Hermite Finite Element Complementing the Bogner-Fox-Schmit Rectangle,"

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