A velocity-based moving mesh virtual element method

Wells, H.; Hubbard, M.E.; Cangiani, A.

Abstract

We present a velocity-based moving mesh virtual element method for the numerical solution of PDEs involving boundaries which are free to move. The virtual element method is used for computing both the mesh velocity and a conservative Arbitrary Lagrangian-Eulerian solution transfer on general polygonal meshes. The approach extends the linear finite element method to polygonal mesh structures, achieving the same degree of accuracy. In the context of moving meshes, a major advantage of the virtual element approach is the ease with which nodes can be inserted on mesh edges. Demonstrations of node insertion techniques are presented to show that moving polygonal meshes can be simply adapted for situations where a boundary encounters a solid object or another moving boundary, without reduction in degree of accuracy.

Citation

Wells, H., Hubbard, M., & Cangiani, A. (2024). A velocity-based moving mesh virtual element method. Computers and Mathematics with Applications, 155, 110-125. https://doi.org/10.1016/j.camwa.2023.12.005

• Journal Article Type: Article
• Acceptance Date: Dec 4, 2023
• Online Publication Date: Dec 12, 2023
• Publication Date: Feb 1, 2024
• Deposit Date: Sep 11, 2024
• Publicly Available Date: Sep 27, 2024
• Journal: Computers and Mathematics with Applications
• Print ISSN: 0898-1221
• Electronic ISSN: 1873-7668
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 155
• Pages: 110-125
• DOI: https://doi.org/10.1016/j.camwa.2023.12.005
• Public URL: https://nottingham-repository.worktribe.com/output/28701576
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0898122123005552?via%3Dihub