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$C^1$ virtual element methods on polygonal meshes with curved edges
- Publication Year :
- 2024
-
Abstract
- In this work we design a novel $C^1$-conforming virtual element method of arbitrary order $k \geq 2$, to solve the biharmonic problem on a domain with curved boundary and internal curved interfaces in two dimensions. By introducing a suitable stabilizing form, we develop a rigorous interpolation, stability, and convergence analysis obtaining optimal error estimates in the energy norm. Finally, we validate the theoretical findings through numerical experiments.<br />Comment: 24 pages, 6 figures
- Subjects :
- Mathematics - Numerical Analysis
65N12, 65N30, 74K20, 35Q74
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.17381
- Document Type :
- Working Paper