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$C^1$ virtual element methods on polygonal meshes with curved edges (2408.17381v2)
Published 30 Aug 2024 in math.NA and cs.NA
Abstract: In this work we design a novel $C1$-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.
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