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- W2023692379 abstract "We develop a method of evaluating element level matrices and vectors associated with p-version finite element computations on tetrahedral meshes with curved boundaries. The procedure uses optimal interpolation formula [Q. Chen, I. Babuška, Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle, Comput. Methods Appl. Mech. Engrg. 128 (1995) 405–417; Q. Chen, I. Babuška, Approximate optimal polynomial interpolation points in the tetrahedron, Comput. Methods Appl. Mech. Engrg. 137 (1997) 89–94] for non-polynomial portions of integrands followed by exact integration. Exact integrals of product combinations of polynomial interpolants and shape functions are stored so that different integrals may be efficiently evaluated by a table look-up. We present error-analysis for our scheme applied to curvilinear tetrahedral meshes with exact geometric representation of the boundary of the domain as defined in a geometric-modelling system. Numerical results are presented for problems involving the Helmholtz equation." @default.
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- W2023692379 date "2006-07-01" @default.
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- W2023692379 title "Integration by table look-up for p-version finite elements on curved tetrahedra" @default.
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- W2023692379 doi "https://doi.org/10.1016/j.cma.2005.10.004" @default.
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