The arbitrary-order virtual element method for linear elastodynamics models. Convergence, stability and dispersion-dissipation analysis.
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Politecnico di Milano (Italy)
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under $$\textit{h}$$-refinement in both the energy and the $L^2$ norms, and optimal error estimates under $$\textit{p}$$-refinement in the energy norm. The performance of the proposed 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 observed under p-refinement. Finally, we present a dispersion-dissipation analysis for both the semi-discrete and fully-discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion-dissipation properties.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA); The Italian Ministry of Education, University and Research (MIUR), Rome (Italy); Istituto Nazionale di Alta Matematica (INdAM), Trieste (Italy); USDOE Laboratory Directed Research and Development (LDRD) Program
- DOE Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1630838
- Report Number(s):
- LA-UR--20-23773
- Country of Publication:
- United States
- Language:
- English
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