# POD reduced-order modeling for evolution equations utilizing arbitrary finite element discretizations

@article{Grle2018PODRM, title={POD reduced-order modeling for evolution equations utilizing arbitrary finite element discretizations}, author={Carmen Gr{\"a}{\ss}le and M. Hinze}, journal={Advances in Computational Mathematics}, year={2018}, volume={44}, pages={1941-1978} }

The main focus of the present work is the inclusion of spatial adaptivity for the snapshot computation in the offline phase of model order reduction utilizing proper orthogonal decomposition (POD-MOR) for nonlinear parabolic evolution problems. We consider snapshots which live in different finite element spaces, which means in a fully discrete setting that the snapshots are vectors of different length. From a numerical point of view, this leads to the problem that the usual POD procedure which… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 60 REFERENCES

POD-Galerkin reduced-order modeling with adaptive finite element snapshots

- Computer Science, Mathematics
- 2016

27

Nonlinear model reduction based on the finite element method with interpolated coefficients: Semilinear parabolic equations

- Mathematics
- 2013

15

An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations

- Mathematics
- 2004

996

An adaptive finite-element Moreau–Yosida-based solver for a non-smooth Cahn–Hilliard problem

- Computer Science, Mathematics
- 2011

48

Missing Point Estimation in Models Described by Proper Orthogonal Decomposition

- Computer Science
- 2008

307

A Minimum-Residual Mixed Reduced Basis Method: Exact Residual Certification and Simultaneous Finite-Element Reduced-Basis Refinement

- Mathematics
- 2016

24

New POD Error Expressions, Error Bounds, and Asymptotic Results for Reduced Order Models of Parabolic PDEs

- Mathematics, Computer Science
- 2014

51