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October 20, 2025Open Access

A Virtual Element Method on polyhedra with curved faces

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Authors

DPDaniele PradaFBFranco BrezziLML. D. Marini

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Overview

This paper reports optimal convergence in virtual element methods for curved boundaries and interfaces, suggesting versatile applications.

Key Points

  • The method achieves optimal convergence rates for degree of accuracy k ≥ 1, ensuring high precision in approximations.
  • Dirichlet and Neumann non-homogeneous boundary conditions can be effectively imposed using this approach.
  • Theoretical analysis is conducted for the two-dimensional case, validated with numerical methods in two and three dimensions.
  • Results support the satisfaction of the patch test when the exact solution is a polynomial of degree k.

Cite This Study

Prada et al. (2025) studied this question.

synapsesocial.com/papers/68f6196ee0bbbc94fac36482https://doi.org/10.48550/arxiv.2509.23005
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