Moving mesh Virtual Element Methods
Publication Date
December 12, 2023
Creator
Abstract
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
ethesis
Thesis Type
PhD
Supervisors
Subjects (LC)
Associated Schools / Departments
School of Mathematical Sciences (UK)
eprints ID
76546
UoN Repository URI
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Harry_Wells_PhD_Thesis.pdf
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Full-text
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