zbMATH — the first resource for mathematics

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.

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