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DOE OSTI · 1669070

The virtual element method for linear elastodynamics models: Design, analysis, and implementation

Antonietti, Paola Francesca·Manzini, Gianmarco·Mourad, Hashem Mohamed·Verani, Marco
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Abstract

We design the conforming virtual element method for the numerical simulation of two dimensional time-dependent elastodynamics problems. We investigate the performance of the method both theoretically and numerically. We prove the stability and the convergence of the semi-discrete approximation in the energy norm and derive optimal error estimates. We also show the convergence in the L 2 norm. The performance of the virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally seen in the p-refinement setting.

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97 MATHEMATICS AND COMPUTINGelastodynamicshigh-order methodsmathematicspolytopal meshvirtual element method

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Antonietti, Paola Francesca, Manzini, Gianmarco, Mourad, Hashem Mohamed, Verani, Marco. 2020-09-27. The virtual element method for linear elastodynamics models: Design, analysis, and implementation. https://doi.org/10.2172/1669070

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