Nielson interpolation operators on an arbitrary triangle with one curved side

1. Barnhill, R.E., Birkhoff, G., Gordon, W.J.: Smooth interpolation in triangles. J. Approx. Theory 8, 114–128 (1973)

   Article  MathSciNet  Google Scholar 

2. Barnhill, R.E.: Blending function interpolation: a survey and some new results. In: Collatz, L., et al. (eds.) Numerishe Methoden der Approximationstheorie, vol. 30, pp. 43–89. Birkhauser-Verlag, Basel (1976)

   Chapter  Google Scholar 

3. Barnhill, R.E.: Representation and approximation of surfaces. In: Rice, J.R. (ed.) Mathematical Software III, pp. 68–119. Academic Press, New-York (1977)

   Google Scholar 

4. Barnhill, R.E., Gregory, J.A.: Sard kernels theorems on triangular domains with applications to finite element error bounds. Numer. Math. 25, 215–229 (1976)

   Article  MathSciNet  Google Scholar 

5. Bernardi, C.: Optimal finite-element interpolation on curved domains. SIAM J. Numer. Anal. 26(5), 1212–1240 (1989)

   Article  MathSciNet  Google Scholar 

6. Blaga, P., Cătinaş, T., Coman, G.: Bernstein-type operators on tetrahedrons, Studia Univ. Babes-Bolyai, Mathematica 54(4), 3–19 (2009)

   MathSciNet  MATH  Google Scholar 

7. Blaga, P., Cătinaş, T., Coman, Gh: Bernstein-type operators on a square with one and two curved sides, Studia Univ. Babes-Bolyai, Mathematica 55(3), 51–67 (2010)

   MATH  Google Scholar 

8. Blaga, P., Cătinaş, T., Coman, G.: Bernstein-type operators on triangle with all curved sides. Appl. Math. Comput. 218, 3072–3082 (2011)

   MathSciNet  MATH  Google Scholar 

9. Blaga, P., Cătinaş, T., Coman, G.: Bernstein-type operators on triangle with one curved side. Mediterr. J. Math. 9(4), 843–855 (2012)

   Article  MathSciNet  Google Scholar 

10. Cătinaş, T.: Some classes of surfaces generated by Nielson and Marshall type operators on the triangle with one curved side. Stud. Univ. Babes-Bolyai Math. 61(3), 305–314 (2016)

    MathSciNet  MATH  Google Scholar 

11. Cătinaş, T.: Extension of some generalized Hermite-type interpolation operators to the triangle with one curved side. Numer. Funct. Anal. Optim. 40(16), 1939–1963 (2019)

    Article  MathSciNet  Google Scholar 

12. Cătinaş, T.: Extension of some particular interpolation operators to a triangle with one curved side. Appl. Math. Comput. 315, 286–297 (2017)

    MathSciNet  MATH  Google Scholar 

13. Cătinaş, T., Blaga, P., Coman, G.: Surfaces generation by blending interpolation on a triangle with one curved side. Results Math. 64(3–4), 343–355 (2013)

    Article  MathSciNet  Google Scholar 

14. Coman, G., Cătinaş, T.: Interpolation operators on a tetrahedron with three curved sides. Calcolo 47(2), 113–128 (2010)

    Article  MathSciNet  Google Scholar 

15. Coman, G., Cătinaş, T.: Interpolation operators on a triangle with one curved side. BIT Numer. Math. 50(2), 243–267 (2010)

    Article  MathSciNet  Google Scholar 

16. Coman, G., Gânscă, I.: Blending approximation with applications in constructions. Bul. Şt. Inst. Politehnic Cluj-Napoca 24, 35–40 (1981)

    MATH  Google Scholar 

17. Coman, G., Gânscă, I.: Some practical application of blending approximation II, Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca (1986)

18. Coman, G., Gânscă, I., Ţâmbulea, L.: Some new roof-surfaces generated by blending interpolation technique. Studia Univ. “Babeş-Bolyai”, Mathematica 36(1), 119–130 (1991)

    MathSciNet  MATH  Google Scholar 

19. Floater, M.S., Schulz, C.: Pointwise radial minimization: Hermite interpolation on arbitrary domains, In: Eurographics Symposium on Geometry Processing, Alliez, P., Rusinkiewicz S., (Eds.), 27(5), (2008)

20. Gordon, W.J., Hall, Ch.: Transfinite element methods: blending-function interpolation over arbitrary curved element domains. Numer. Math. 21, 109–129 (1973)

    Article  MathSciNet  Google Scholar 

21. Gordon, W.J., Wixom, J.A.: Pseudo-harmonic interpolation on convex domains. SIAM J. Numer. Anal. 11(5), 909–933 (1974)

    Article  MathSciNet  Google Scholar 

22. Gregory, J.A.: A blending function interpolant for triangles. In: Handscomb, D.C. (ed.) Multivariate Approximation, pp. 279–287. Academic Press, London (1978)

    Google Scholar 

23. Liu, B., Liu, C., Lu, S., Wua, Y., Xinga, Y., Ferreira, A.J.M.: A differential quadrature hierarchical finite element method using Fekete points for triangles and tetrahedrons and its applications to structural vibration. Comput. Methods Appl. Mech. Eng. 349, 798–838 (2019)

    Article  MathSciNet  Google Scholar 

24. Marshall, J.A., McLeod, R.: Curved elements in the finite element method. In: Conference on Numerical Solution Differential Equation, Lectures Notes in Mathematics, 363, Springer Verlag, pp. 89-104 (1974)

25. Marshall, J.A., Mitchell, A.R.: Blending interpolants in the finite element method. Inter. J. Numer. Methods Eng. 12, 77–83 (1978)

    Article  MathSciNet  Google Scholar 

26. Nielson, G.M.: Minimum norm interpolation in triangles. SIAM J. Numer. Anal. 17(1), 44–62 (1980)

    Article  MathSciNet  Google Scholar 

27. Renka, R.J., Cline, A.K.: A triangle-based \(C^{1}\) interpolation method. Rocky Mt. J. Math. 14, 223–237 (1984)

    Article  Google Scholar 

28. Sard, A.: Linear Approximation. AMS, Providence, RI (1963)

    Book  Google Scholar 

29. Zlamal, M.: Curved elements in the finite element method. SIAM J. Numer. Anal. 10(1), 229–240 (1973)

    Article  MathSciNet  Google Scholar 

Download references