WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 23, 2024
Equivalence between $$C^{1}$$-continuous Cubic B-splines and Cubic Hermite Polynomials in Finite Element and Collocation Methods
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Abstract: In this paper, we will show that the $$C^{1}$$-continuous B-spline functional set of polynomial degree , can be written as a linear transformation of the well-known piecewise cubic Hermite polynomials. This change of functional basis means that the global B-spline finite element solution is equivalent to that of usual piecewise finite elements in conjunction with cubic Hermite polynomials, with two degrees per nodal point, like those used in beam-bending analysis. In this context, we validate the equivalence between the global B-spline solution and the piecewise solution in boundary-value and eigenvalue problems, for collocation and Ritz-Galerkin methods.
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Keywords: Finite element method, Ritz-Galerkin method, Collocation method, B-spline, Hermite polynomials, Knot insertion, Bézier extraction, wave equation, Boundary-value problem, Computational mechanics
Pages: 585-597
DOI: 10.37394/23202.2024.23.60