Virtual Element Methods for hyperbolic problems on polygonal meshes. (1st September 2017)

• Record Type: Journal Article
• Authors: Vacca, Giuseppe
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 5(2017)
• Page Start: 882
• Page End: 898
• Publication Date: 2017-09-01
• Subjects: Virtual Element Methods -- Hyperbolic problems -- Polygonal meshes -- Wave propagation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.04.029
• Languages: English
• ISSNs: 0898-1221

Abstract

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 set of numerical tests.