Moving mesh Virtual Element Methods

Wells, Harry (2023) Moving mesh Virtual Element Methods. PhD thesis, University of Nottingham.

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This thesis explores the development and analysis of moving mesh Virtual Element Methods for partial differential equations on time-dependent domains. This thesis presents the first moving mesh method to purely use the Virtual Element Method, an isoparametric Virtual Element Method for approximating partial differential equations on curved domains and a high-order Arbitrary Lagrangian-Eulerian Virtual Element Method for problems on time-dependent domains with moving boundaries. Each contribution successfully demonstrates the applicability and accuracy of Virtual Element Methods in existing moving mesh algorithms, achieving similar orders of accuracy compared to classical Finite Element Method approaches. The results suggest that the flexibility of moving mesh methods can be greatly improved by incorporating more general mesh structures, including polygons and curved-edged polygons, proving the Virtual Element Method offers an effective extension to classical approaches. This work provides a foundation for future research in Virtual Element Methods for more complex problems on time-dependent domains and developing the analysis to support proposed moving mesh methods.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Hubbard, Matthew
Cangiani, Andrea
Keywords: Partial differential equations; Time-dependent domains; Moving boundaries; Moving mesh algorithms
Subjects: Q Science > QA Mathematics
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 76546
Depositing User: Wells, Harry
Date Deposited: 12 Dec 2023 04:40
Last Modified: 12 Dec 2023 04:40

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