Non-Isotropic Jacobi Spectral and Pseudospectral Methods in Three Dimensions (Journal of Mathematical Study, 2015)
Non-isotropic Jacobi orthogonal approximation and Jacobi-Gauss type interpolationin three dimensions are investigated. The basic approximation results areestablished, which serve as the mathematical foundation of spectral and pseudospectralmethods for singular problems, as well as problems defined on axisymmetric domainsand some unbounded domains. The spectral and pseudospectral schemes areprovided for two model problems. Their spectral accuracy is proved. Numerical resultsdemonstrate the high efficiency of suggested algorithms.
Keywords: Jacobi spectral and pseudospectral methods in three dimensions; singular problems.