Geodesic
Convergence analysis of Galerkin POD for linear second order evolution equations
Electronic transactions on numerical analysis, Tome 40 (2013), pp. 321-337
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},
     year = {2013},
     volume = {40},
     zbl = {1290.65090},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2013__40__a9/}
}
TY  - JOUR
AU  - Herkt,  Sabrina
AU  - Hinze,  Michael
AU  - Pinnau,  Rene
TI  - Convergence analysis of Galerkin POD for linear second order evolution equations
JO  - Electronic transactions on numerical analysis
PY  - 2013
SP  - 321
EP  - 337
VL  - 40
UR  - http://geodesic.mathdoc.fr/item/ETNA_2013__40__a9/
LA  - en
ID  - ETNA_2013__40__a9
ER  - 
%0 Journal Article
%A Herkt,  Sabrina
%A Hinze,  Michael
%A Pinnau,  Rene
%T Convergence analysis of Galerkin POD for linear second order evolution equations
%J Electronic transactions on numerical analysis
%D 2013
%P 321-337
%V 40
%U http://geodesic.mathdoc.fr/item/ETNA_2013__40__a9/
%G en
%F ETNA_2013__40__a9
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/