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.