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Non-isotropic Jacobi orthogonal approximation and Jacobi-Gauss type interpolation in three dimensions are investigated. The basic approximation results are established, which serve as the mathematical foundation of spectral and pseudospectral methods for singular problems, as well as problems defined on axisymmetric domains and some unbounded domains. The spectral and pseudospectral schemes are provided for two model problems. Their spectral accuracy is proved. Numerical results demonstrate the high efficiency of suggested algorithms.
}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n3.15.02}, url = {http://global-sci.org/intro/article_detail/jms/9922.html} }Non-isotropic Jacobi orthogonal approximation and Jacobi-Gauss type interpolation in three dimensions are investigated. The basic approximation results are established, which serve as the mathematical foundation of spectral and pseudospectral methods for singular problems, as well as problems defined on axisymmetric domains and some unbounded domains. The spectral and pseudospectral schemes are provided for two model problems. Their spectral accuracy is proved. Numerical results demonstrate the high efficiency of suggested algorithms.