The proper orthogonal decomposition modal spectral element method for two-dimensional viscoelastic equation

A reduced order modal spectral element method has been investigated to solve a two-dimensional viscoelastic equation. The reduced order technique is based upon the proper orthogonal decomposition (POD) method. The basis functions are derived from Legendre orthogonal polynomials. First, the time-discrete plan is constructed using the Crank-Nicolson idea. Then, the stability and convergence of the time-discrete formulation have been analyzed by the energy method. An error estimate of the fully-discrete scheme is provided and numerical experiments confirm that the new scheme needs less running CPU time than the classical modal spectral element procedure.

Automated summary

A reduced order modal spectral element method for solving a viscoelastic equation in two dimensions is proposed, utilizing the proper orthogonal decomposition (POD) method and Legendre orthogonal polynomials. It is shown through numerical experiments that this new method requires less CPU time than the classical approach.