Uniformly polynomially stable approximations for a class of second order evolution equations

TL;DR

This paper demonstrates that adding a numerical viscosity term to semi-discrete schemes for certain damped vibration systems ensures uniform polynomial stability across discretization parameters, improving approximation reliability.

Contribution

It introduces a novel numerical viscosity approach that guarantees uniform polynomial stability in semi-discrete approximations of second order evolution equations.

Findings

Numerical viscosity ensures uniform polynomial stability

Semi-discrete schemes accurately approximate damped vibrations

Stability is maintained independently of discretization size

Abstract

In this paper we study time semi-discrete approximations of a class of polynomially stable infinite dimensional systems modeling the damped vibrations. We prove that adding a suitable numerical viscosity term in the numerical scheme, one obtains approximations that are uniformly polynomially stable with respect to the discretization parameter.