Abstract
In this chapter we study the concept of a finite element in some more detail. We begin with the classical definition of a finite element as the triplet of a polygon, a polynomial space, and a set of functionals. We then show how to derive shape functions for the most common Lagrange elements. The isoparametric mapping is introduced as a tool to allow for elements with curved boundaries, and to simplify the computation of the element stiffness matrix and load vector. We finish by presenting some more exotic elements.
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References
P. Ciarlet. The Finite Element Method for Elliptic Problems. Classics in Applied Mathematics, 40. SIAM, 2002.
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Larson, M.G., Bengzon, F. (2013). The Finite Element. In: The Finite Element Method: Theory, Implementation, and Applications. Texts in Computational Science and Engineering, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33287-6_8
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DOI: https://doi.org/10.1007/978-3-642-33287-6_8
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-642-33287-6
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