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R. A. Adams and J. J. F. Fournier, “Sobolev Spaces,” Academic Press, New York, 2003.

has been cited by the following article:

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

  AUTHORS: Lidia Gileva, Vladimir Shaydurov, Boris Dobronets

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

  JOURNAL NAME: Applied Mathematics, Vol.4 No.12A, December 24, 2013

  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.