×

Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems. (English) Zbl 1156.35020

Summary: Proper orthogonal decomposition (POD) is a powerful technique for model reduction of linear and non-linear systems. It is based on a Galerkin type discretization with basis elements created from the system itself. In this work, error estimates for Galerkin POD methods for linear elliptic, parameter-dependent systems are proved. The resulting error bounds depend on the number of POD basis functions and on the parameter grid that is used to generate the snapshots and to compute the POD basis. The error estimates also hold for semi-linear elliptic problems with monotone nonlinearity. Numerical examples are included.

MSC:

35J45 Systems of elliptic equations, general (MSC2000)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI Link