It is well known that Lagrange interpolation based on equispaced nodes can yield poor results. Oscillations may appear when using high degree polynomials. For functions of one variable, the most celebrated example has been provided by Carl Runge in 1901, who showed that higher degrees do not always improve interpolation accuracy. His example was then extended to multivariate calculus and in this work we show that it is meaningful, in an appropriate sense, also for Whitney edge elements, namely for differential 1-forms.
Whitney edge elements and the Runge phenomenon / Alonso Rodríguez, Ana; Bruni Bruno, Ludovico; Rapetti, Francesca. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - ELETTRONICO. - 427:(2023), pp. 1151171-1151179. [10.1016/j.cam.2023.115117]
Whitney edge elements and the Runge phenomenon
Alonso Rodríguez, Ana;Bruni Bruno, Ludovico
;Rapetti, Francesca
2023-01-01
Abstract
It is well known that Lagrange interpolation based on equispaced nodes can yield poor results. Oscillations may appear when using high degree polynomials. For functions of one variable, the most celebrated example has been provided by Carl Runge in 1901, who showed that higher degrees do not always improve interpolation accuracy. His example was then extended to multivariate calculus and in this work we show that it is meaningful, in an appropriate sense, also for Whitney edge elements, namely for differential 1-forms.| File | Dimensione | Formato | |
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