The Serendipity Family of Finite Elements
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We give a new, simple, dimension-independent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s−r of the variables where s is the degree of the monomial or, equivalently, whose superlinear degree (total degree with respect to variables entering at least quadratically) is at most r. The degrees of freedom are given by moments of degree at most r−2d on each face of dimension d. We establish unisolvence and a geometric decomposition of the space.
- T.J.R. Hughes, The Finite Element Method (Englewood Cliffs, Prentice-Hall, 1987). Linear static and dynamic finite element analysis, with the collaboration of Robert M. Ferencz and Arthur M. Raefsky.
- V.N. Kaliakin, Introduction to Approximate Solution Techniques, Numerical Modeling, & Finite Element Methods (CRC Press, Boca Raton, 2001). Civil and Environmental Engineering.
- J. Mandel, Iterative solvers by substructuring for the p-version finite element method, Comput. Methods Appl. Mech. Eng. 80(1–3), 117–128 (1990). Spectral and high order methods for partial differential equations (Como, 1989). CrossRef
- G. Strang, G.J. Fix, An analysis of the finite element method, in Prentice-Hall Series in Automatic Computation (Prentice-Hall, Englewood Cliffs, 1973).
- B. Szabó, I. Babuška, Finite Element Analysis (Wiley-Interscience, New York, 1991).
- O.C. Zinkiewicz, R.L. Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th edn., vol. 1 (Butterworth, Stoneham, 2005).
- The Serendipity Family of Finite Elements
Foundations of Computational Mathematics
Volume 11, Issue 3 , pp 337-344
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