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NURBS-based geometries: a mapping approach for virtual serendipity elements. (English) Zbl 1506.74452

Summary: A NURBS-based serendipity virtual element method for general (arbitrary) element shapes is outlined in this work. The low-order VEM ansatz function is now extended towards higher-order formulation. In comparison with the already existing serendipity VEM, a general mapping scheme is developed within this contribution allowing to deviate from the assumption of straight edges of virtual elements. A number of numerical examples illustrates the robustness and accuracy of the new mapping methodology. The results are very promising and underline the advantages of the formulations for dealing with arbitrary geometries.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65D07 Numerical computation using splines

Software:

AceFEM; AceGen
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Full Text: DOI

References:

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