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Piecewise polynomials with different smoothness degrees on polyhedral complexes
Date
2019-05-01
Author
ALTINOK BHUPAL, SELMA
Sipahi, Neslihan Os
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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For a given d-dimensional polyhedral complex Delta and a given degree k, we consider the vector space of piecewise polynomial functions on Delta of degree at most k with a different smoothness condition on each pair of adjacent d-faces of Delta. This is a finite dimensional vector space. The fundamental problem in Approximation Theory is to compute the dimension of this vector space. It is known that the dimension is given by a polynomial for sufficiently large k via commutative algebra. By using the technique of McDonald and Schenck [3] and extending their result to a plane polyhedral complex Delta with varying smoothness conditions, we determine this polynomial. This gives a complete answer for the dimension. At the end we discuss some examples through this technique.
Subject Keywords
Mathematics (miscellaneous)
URI
https://hdl.handle.net/11511/65897
Journal
QUAESTIONES MATHEMATICAE
DOI
https://doi.org/10.2989/16073606.2018.1481464
Collections
Department of Mathematics, Article
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S. ALTINOK BHUPAL and N. O. Sipahi, “Piecewise polynomials with different smoothness degrees on polyhedral complexes,”
QUAESTIONES MATHEMATICAE
, pp. 673–685, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65897.