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A nodal basis for $ C^{1}$ piecewise polynomials of degree $ n\geq 5$

Authors: John Morgan and Ridgway Scott
Journal: Math. Comp. 29 (1975), 736-740
MSC: Primary 65D15
MathSciNet review: 0375740
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Abstract: A basis for the space of $ {C^1}$ piecewise polynomials in two variables of degree $ n \geqslant 5$ is constructed. The basis is parametrized by "nodal variables," namely, the values and derivatives of the basis functions at a discrete set of points.

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  • [1] J.-P. AUBIN, Approximation of Elliptic Boundary-Value Problems, Wiley, New York, 1972. MR 0478662 (57:18139)
  • [2] J. MORGAN & R. SCOTT, "The dimension of the space of $ {C^1}$ piecewise polynomials." (To appear.)
  • [3] G. STRANG, "Piecewise polynomials and the finite element method," Bull. Amer. Math. Soc., v. 79, 1973, pp. 1128-1137. MR 48 #5402. MR 0327060 (48:5402)
  • [4] G. STRANG & G. FIX, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, N. J., 1973. MR 0443377 (56:1747)

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Article copyright: © Copyright 1975 American Mathematical Society

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