Hansen, Glen; Zardecki, Andrew; Greening, Doran; Bos, Randy A finite element method for three-dimensional unstructured grid smoothing. (English) Zbl 1061.65133 J. Comput. Phys. 202, No. 1, 281-297 (2005). Summary: The finite element method is applied to grid smoothing in three-dimensional geometry, generalizing earlier results obtained for planar geometry. The underlying set of equations for the Cartesian components of grid coordinates, based on the notion of harmonic coordinates, has a natural variational formulation. To estimate the target metric tensor that drives the elliptic grid equations, the metric tensor components are computed on a coarse-grained grid. Numerical examples illustrating the proposed approach are presented together with results from the smoothness functional, which is used to measure the quality of the resulting grid. Cited in 1 ReviewCited in 11 Documents MSC: 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:Finite elements; Galerkin methods; Mesh generation; Elliptic smoothing; elliptic grid equations; numerical examples Software:BPKit PDFBibTeX XMLCite \textit{G. Hansen} et al., J. Comput. Phys. 202, No. 1, 281--297 (2005; Zbl 1061.65133) Full Text: DOI References: [1] Knupp, P.; Steinberg, S., Fundamentals of Grid Generation (1994), CRC Press: CRC Press Boca Raton, FL · Zbl 0855.65123 [2] Hansen, G.; Zardecki, A.; Greening, D.; Bos, R., A finite element method for unstructured grid smoothing, J. Comput. 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