Virtual Element Methods for General Linear Second-order Hyperbolic Problems on Polygonal Meshes

Abstract

This thesis focuses on the development of Virtual Element Methods (VEM) for the general linear second-order hyperbolic problems on polygonal meshes. These problems arise in many areas of science and engineering, including fluid dynamics, acoustics, and electro-magnetics. The primary focus of this work is to analyse the convergence of virtual element approximations to the exact solutions for both semi-discrete and fully-discrete formulation. In addition to the standard wave equations, these problems involve additional damping terms (weak damping and/or strong damping terms) and require further analyses to derive optimal convergence results.