Virtual element methods for weakly damped wave equations on polygonal meshes

We develop a virtual element method for weakly damped wave equations on polygonal meshes. Very general polygonal meshes are used for the spatial discretization. In both L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}$$\end{document} norm and H1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{1}$$\end{document} semi-norm, optimal order of convergence is obtained for the spatially discrete approximation. We employ the Crank–Nicolson temporal discretization scheme for the fully discrete problem and derive the convergence analysis. Numerical experiments are illustrated to confirm our theoretical findings.