Piecewise polynomials with different smoothness degrees on polyhedral complexes

Date

2019-05-01

Author

ALTINOK BHUPAL, SELMA
Sipahi, Neslihan Os

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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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Citation Formats

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.