A Virtual Element Method on polyhedra with curved faces

Daniele Prada; Franco Brezzi; L. Donatella Marini

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arXiv · 2509.23005

A Virtual Element Method on polyhedra with curved faces

Daniele Prada·Franco Brezzi·L. Donatella Marini

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Abstract

In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann non-homogeneous boundary conditions, and provides, for degree of accuracy $k \geq 1$, optimal convergence rates. Whenever the exact solution is a polynomial of degree $k$, local spaces of degree $k$ ensure satisfaction of the patch test. The proposed method is theoretically analyzed in the two-dimensional case, whereas it is numerically validated both in two and three dimensions.

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Daniele Prada, Franco Brezzi, L. Donatella Marini. 2025-09-26. A Virtual Element Method on polyhedra with curved faces. https://arxiv.org/abs/2509.23005

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