Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems

By M. Kahlbacher, Stefan Volkwein. 2007

80 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Proper Orthogonal Decomposition for Linear-Quadratic Optimal Control (2013, background): “, to [20, 22, 30, 39, 40, 41, 63] and [33], where POD Galerkin schemes for parabolic equations and elliptic equations are studied.”
Low-rank methods for high-dimensional approximation and model order reduction (2015, unknown): “n then be used for computing an approximation of u(ξ) in Vr for all ξ∈ Ξ. This approach is at the basis of Galerkin Proper Orthogonal Decomposition methods for parameter-dependent equations (see e.g. [49]). Case p= ∞. For p= ∞, the best rank-rapproximation is well deﬁned and the corresponding error ”
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples (2012, methodology): “The reduced basis [20, 21, 23, 24, 27] and the proper orthogonal decomposition (POD) [12,15, 17, 19, 28] are two techniques belonging to this second family.”
Approximation of high-dimensional parametric PDEs * (2015, methodology): “We refer to [52] for a general introduction on the related POD method, which is not discussed in our paper.”