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- Title
A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations.
- Authors
Mora, David; Rivera, Gonzalo
- Abstract
We present a priori and a posteriori error analyses of a virtual element method (VEM) to approximate the vibration frequencies and modes of an elastic solid. We analyse a variational formulation relying only on the solid displacement and propose an |$H^{1}(\Omega)$| -conforming discretization by means of the VEM. Under standard assumptions on the computational domain, we show that the resulting scheme provides a correct approximation of the spectrum and prove an optimal–order error estimate for the eigenfunctions and a double order for the eigenvalues. Since the VEM has the advantage of using general polygonal meshes, which allows efficient implementation of mesh refinement strategies, we also introduce a residual-type a posteriori error estimator and prove its reliability and efficiency. We use the corresponding error estimator to drive an adaptive scheme. Finally, we report the results of a couple of numerical tests that allow us to assess the performance of this approach.
- Subjects
A posteriori error analysis; SPECTRAL element method; ERROR analysis in mathematics; ELASTICITY; ELASTIC solids; FREQUENCIES of oscillating systems; EQUATIONS; ESTIMATES
- Publication
IMA Journal of Numerical Analysis, 2020, Vol 40, Issue 1, p322
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/dry063