Virtual Element Methods for hyperbolic problems on polygonal meshes

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.

References in corpus (4)

• A Virtual Element Method for elastic and inelastic problems on polytope meshes
• Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes
• A $C^1$ virtual element method for the Cahn-Hilliard equation with polygonal meshes
• Mimetic Finite Difference methods for Hamiltonian wave equations in 2D

Cited by in corpus (2)

• A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem
• The virtual element method for linear elastodynamics models. Convergence, stability and dissipation-dispersion analysis