Abstract
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.
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