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arXiv · 1602.05781

Virtual Element Methods for hyperbolic problems on polygonal meshes

Giuseppe Vacca
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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.

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Giuseppe Vacca. 2016-02-18. Virtual Element Methods for hyperbolic problems on polygonal meshes. https://arxiv.org/abs/1602.05781

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