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**Spectral/hp element methods for CFD.**
*(English)*
Zbl 0954.76001

Numerical Mathematics and Scientific Computation. Oxford: Oxford University Press. x, 390 p. (1999).

The authors describe how to use spectral/hp element methods for solving the problems of computational fluid dynamics. A particular emphasis is given to their applications on unstructured meshes. The need to find accurate solutions to the viscous flow equations around complex aerodynamic configurations has led to the development of high-order discretizations. They also are efficient for the calculation of time-dependent oscillatory solutions over long time periods, for example, in the new field of computational electromagnetics in aerospace design. The authors introduce spectral and hp element methods on structured and unstructured meshes, together with construction of geometrically non-conforming elements. These methods are applied to advection and Helmholtz equations. Applications are also given to incompressible and compressible flow problems.

Reviewer: W.Heinrichs (Essen)

### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76M22 | Spectral methods applied to problems in fluid mechanics |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

76M10 | Finite element methods applied to problems in fluid mechanics |