Abstract
In this paper, the orthogonal polynomial approximation on triangle, proposed by Dubiner, is studied. Some approximation results are established in certain non-uniformly Jacobi-weighted Sobolev space, which play important role in numerical analysis of spectral and triangle spectral element methods for differential equations on complex geometries. As an example, a model problem is considered.
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Communicated by Z.Y. Chen
Mathematics subject classifications (2000)
33C45, 41A10, 41A25, 65N35
Ben-yu Guo: The work of this author is supported in part by NSF of China, N.10471095, Science Foundation of Shanghai, N. 04JC14062, The Special Funds for Doctorial Authorities of Education Ministry of China, N. 20040270002, E-institutes of Shanghai Municipal Education Commission, N.E03004, The Shanghai Leading Academic Discipline Project N. T0401 and The Fund N.04DB15 of Shanghai Education Commission.
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Guo, By., Wang, LL. Error analysis of spectral method on a triangle. Adv Comput Math 26, 473–496 (2007). https://doi.org/10.1007/s10444-005-7471-8
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DOI: https://doi.org/10.1007/s10444-005-7471-8