Mixed Virtual Element approximation of linear acoustic wave equation

09/23/2022
by   Franco Dassi, et al.
0

We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time the semi-discrete problem we consider a classical theta-method scheme. We carry out the stability and convergence analysis in the energy norm for the semi-discrete problem showing optimal rate of convergence with respect to the mesh size. We further study the property of energy conservation for the fully-discrete system. Finally, we present some verification tests as well as engineering application of the method.

READ FULL TEXT

page 15

page 20

page 21

page 22

research
11/22/2021

A higher order nonconforming virtual element method for the Cahn-Hilliard equation

In this paper we develop a fully nonconforming virtual element method (V...
research
09/06/2022

Mixed approximation of nonlinear acoustic equations: Well-posedness and a priori error analysis

Accurate simulation of nonlinear acoustic waves is essential for the con...
research
12/15/2019

The virtual element method for linear elastodynamics models. Design, analysis, and implementation

We design the conforming virtual element method for the numerical simula...
research
09/16/2020

Strong convergence of a Verlet integrator for the semi-linear stochastic wave equation

The full discretization of the semi-linear stochastic wave equation is c...
research
10/20/2021

A C^0 interior penalty method for mth-Laplace equation

In this paper, we propose a C^0 interior penalty method for mth-Laplace ...
research
07/12/2021

A conservative and energy stable discontinuous spectral element method for the shifted wave equation in second order form

In this paper, we develop a provably energy stable and conservative disc...
research
03/19/2023

A virtual element method for the solution of 2D time-harmonic elastic wave equations via scalar potentials

In this paper, we propose and analyse a numerical method to solve 2D Dir...

Please sign up or login with your details

Forgot password? Click here to reset