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Tetrahedral $$hp$$ finite elements: Algorithms and flow simulations. (English) Zbl 0847.76038
Summary: We present a new discretization for the incompressible Navier-Stokes equations that extends spectral methods to three-dimensional complex domains consisting of tetrahedral subdomains. The algorithm is based on standard concepts of $$hp$$ finite elements as well as tensorial spectral elements. The new formulation employs a hierarchical/modal basis constructed from a new apex coordinate system which retains a generalised tensor product. These properties enable the development of computationally efficient algorithms for use on standard finite volume unstructured meshes.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids
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