A study on Sobolev orthogonal polynomials on a triangle

AKTAŞ KARAMAN R., Lekesiz E. G., AYGAR KÜÇÜKEVCİLİOĞLU Y.

NUMERICAL ALGORITHMS, cilt.97, sa.2, ss.915-944, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 97 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s11075-023-01732-5
  • Dergi Adı: NUMERICAL ALGORITHMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.915-944
  • Anahtar Kelimeler: Inner product, Jacobi polynomials, Orthogonality, Sobolev space, Triangle
  • Ankara Üniversitesi Adresli: Evet

Özet

The main aim of this paper is to investigate Sobolev orthogonality and families of orthogonal polynomials on the triangle as a generalization of the results in Xu, Y. Constr. Approx. 46, 349-434 (2017). We define inner products or pseudo-inner products that contain derivatives up to third-order in the Sobolev space on a triangle and study associated orthogonal polynomials that are analogs of the Jacobi polynomials J(alpha,beta,gamma) (k,n) but with alpha,beta,gamma being -1, -2, or -3, and two other families derived under simultaneous permutations of (x,y,1-x-y) and (alpha,beta,gamma).