Construction of a normalized basis of a univariate quadratic $C^1$ spline space and application to the quasi-interpolation
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In this paper, we use the finite element method to construct a new normalized basis of a univariate quadratic $C^1$ spline space. We give a new representation of Hermite interpolant of any piecewise polynomial of class at least $C^1$ in terms of its polar form. We use this representation for constructing several superconvergent and super-superconvergent discrete quasi-interpolants which have an optimal approximation order. This approach is simple and provides an interesting approximation. Numerical results are given to illustrate the theoretical ones.
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2011 ◽
Vol 250-253
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pp. 3872-3875
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2020 ◽
Vol 7
(10)
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pp. 458-470
2019 ◽
Vol 233
(16)
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pp. 5568-5584
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2014 ◽
Vol 229
(8)
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pp. 1385-1398
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2016 ◽
Vol 21
(3)
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pp. 569-580
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