Geodesic
Convergence analysis of Galerkin POD for linear second order evolution equations
Electronic transactions on numerical analysis, Tome 40 (2013), pp. 321-337.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34A05
Keywords: wave equation, POD, error estimates 
@article{ETNA_2013__40__a9,
     author = {Herkt, Sabrina and Hinze, Michael and Pinnau, Rene},
     title = {Convergence analysis of {Galerkin} {POD} for linear second order evolution equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {321--337},
     publisher = {mathdoc},
     volume = {40},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2013__40__a9/}
}
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Herkt, Sabrina; Hinze, Michael; Pinnau, Rene. Convergence analysis of Galerkin POD for linear second order evolution equations. Electronic transactions on numerical analysis, Tome 40 (2013), pp. 321-337. http://geodesic.mathdoc.fr/item/ETNA_2013__40__a9/