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

Technical Report · Sun Sep 27 00:00:00 EDT 2020

DOI:https://doi.org/10.2172/1669070· OSTI ID:1669070

Antonietti, Paola Francesca ^[1]; Manzini, Gianmarco ^[2]; Mourad, Hashem Mohamed ^[2]; Verani, Marco ^[1]

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1. Politecnico di Milano (Italy)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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 L² 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.

• Research Organization: Politecnico di Milano (Italy); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program; Ministry of Education, University and Research (MIUR)
• DOE Contract Number: 89233218CNA000001
• OSTI ID: 1669070
• Report Number(s): LA-UR--19-29577
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
elastodynamics
high-order methods
mathematics
polytopal mesh
virtual element method