Cut finite element error estimates for a class of nonliner elliptic PDEs

Katsouleas, Georgios; Karatzas, Efthymios N.; Travlopanos, Fotios

doi:10.17028/rd.lboro.12154854.v1

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Imex Type Time Discretization1

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2020

2022

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Cited by 3 publications

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“…We fully discretize the system by an IMEX approach, see e.g. [67] and references therein, as well as [57] for similar types of nonlinearities. Approximations will be constructed on a time partition 0 = t 0 < t 1 < .…”

Section: Imex Type Time Discretizationmentioning

confidence: 99%

A reduced order model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements

Karatzas¹,

Rozza²

2020

Preprint

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In the present work, we investigate for the first time with a cut finite element method, a parameterized 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.

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Section: Imex Type Time Discretizationmentioning

confidence: 99%