Virtual Element Methods for hyperbolic problems on polygonal meshes
Numerical Analysis
2016-02-19 v1
Abstract
In the present paper we develop the Virtual Element Method for hyperbolic problems on polygonal meshes, considering the linear wave equations as our model problem. After presenting the semi-discrete scheme, we derive the convergence estimates in H^1 semi-norm and L^2 norm. Moreover we develop a theoretical analysis on the stability for the fully discrete problem by comparing the Newmark method and the Bathe method. Finally we show the practical behaviour of the proposed method through a large array of numerical tests.
Cite
@article{arxiv.1602.05781,
title = {Virtual Element Methods for hyperbolic problems on polygonal meshes},
author = {Giuseppe Vacca},
journal= {arXiv preprint arXiv:1602.05781},
year = {2016}
}