A Spectral Method for Mixed Boundary Value Problems on Hexahedrons

Abstract

In this paper, we investigate a spectral method for mixed boundary value problems defined on hexahedrons. Some results on irrational orthogonal approximation are established, which play important roles in numerical solutions of partial differential equations defined on hexahedrons. As examples of applications, we provide spectral schemes for two model problems, and prove their spectral accuracy. Efficient numerical implementations are described. Numerical results demonstrate the high efficiency of suggested algorithms.