Convergence Analysis of Galerkin POD for linear second order evolution equations

Abstract. In this paper, we investigate the proper orthogonal decomposition (POD) discretization method for linear second order evolution equations. We present error estimates for two different choices of snapshot sets, one consisting of solution snapshots only and one consisting of solution snapshots and their derivatives up to second order. We show that the results of [Numer. Math., 90 (2001), pp. 117–148] for parabolic equations can be extended to linear second order evolution equations, and that the derivative snapshot POD method behaves better than the classical one for small time steps. Numerical comparisons of the different approaches are presented, illustrating the theoretical results.

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