Error analysis of spectral method on a triangle
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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.
Keywordsspectral method on triangle convergence
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- P. Appell and J. Kampé de Fériet, Functions hypergéométriques et hyperspheriques-polynomes d'Hermite (Gauthier-Villars, Paris, 1926). Google Scholar
- I. Babuška and B.Q. Guo, Direct and inverse approximation theorems for the p-version of the finite element method in the framework of weighted Besov spacecs, part I, approximability of functions in weighted Besov spaces, SIAM J. Numer. Anal. 39 (2001) 1512–1538. MathSciNetCrossRefzbMATHGoogle Scholar
- C. Bernardi and Y. Maday, Spectral method, in: Handbook of Numerical Analysis, Part 5, eds. P.G. Ciarlet and J.L. Lions (North-Holland, Amsterdam, 1977). Google Scholar
- D. Funaro, Polynomial Approximations of Differential Equations (Springer-Verlag, Berlin, 1992). Google Scholar
- B.-y. Guo and L.-L. Wang, Non-isotropic Jacobi spectral method, in: Contemporary Mathematics, Vol. 329 (Amer. Math. Soc., Providence, RI, 2003) pp. 157–169. Google Scholar
- G. Szegö, Othogonal Polynomials, Vol. 23, 4th edn. (AWS Coll. Publ., 1975). Google Scholar