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- W4287673401 abstract "In the present work, we investigate a cut finite element method for the parameterized system of second-order equations stemming from the splitting approach of a fourth order nonlinear geometrical PDE, namely the Cahn-Hilliard system. We manage to tackle the instability issues of such methods whenever strong nonlinearities appear and to utilize their flexibility of the fixed background geometry -- and mesh -- characteristic, through which, one can avoid e.g. in parametrized geometries the remeshing on the full order level, as well as, transformations to reference geometries on the reduced level. As a final goal, we manage to find an efficient global, concerning the geometrical manifold, and independent of geometrical changes, reduced order basis. The POD-Galerkin approach exhibits its strength even with pseudo-random discontinuous initial data verified by numerical experiments." @default.
- W4287673401 created "2022-07-25" @default.
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- W4287673401 date "2020-09-03" @default.
- W4287673401 modified "2023-09-27" @default.
- W4287673401 title "A reduced order model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements" @default.
- W4287673401 doi "https://doi.org/10.48550/arxiv.2009.01596" @default.
- W4287673401 hasPublicationYear "2020" @default.
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