Space-Time Galerkin POD with Application in Optimal Control of Semilinear Partial Differential Equations

@article{Baumann2018SpaceTimeGP,
title={Space-Time Galerkin POD with Application in Optimal Control of Semilinear Partial Differential Equations},
author={Manuel Baumann and Peter Benner and Jan Heiland},
journal={SIAM J. Scientific Computing},
year={2018},
volume={40}
}

In the context of Galerkin discretizations of a partial differential equation (PDE), the modes of the classical method of proper orthogonal decomposition (POD) can be interpreted as the ansatz and trial functions of a low-dimensional Galerkin scheme. If one also considers a Galerkin method for the time integration, one can similarly define a POD reduction of the temporal component. This has been described earlier but not expanded upon—probably because the reduced time discretization globalizes… CONTINUE READING

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