Piecewise polynomials with different smoothness degrees on polyhedral complexes


ALTINOK BHUPAL S., Sipahi N. O.

QUAESTIONES MATHEMATICAE, cilt.42, ss.673-685, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 42 Konu: 5
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2989/16073606.2018.1481464
  • Dergi Adı: QUAESTIONES MATHEMATICAE
  • Sayfa Sayıları: ss.673-685

Özet

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.