Abstract
Surface interpolation is used to produce basis functions for two-dimensional curved finite elements. The connection between rational surfaces and isoparametric methods is discussed with the occurrence of the Steiner surface being highlighted. A corollary to Max Noether's intersection theorem is used to produce high order stable bases. Parametric cubic curves are discussed from a geometrical viewpoint and this viewpoint is used to develop transfinite blending functions for a wide variety of shapes.
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© 1982 Springer-Verlag
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McLeod, R.J.Y. (1982). Some applications of geometry in numerical analysis. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093158
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DOI: https://doi.org/10.1007/BFb0093158
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