---
abstract: 'We deal with the virtual element method (VEM) for solving the Poisson equation on a domain $\Omega$ with curved boundaries. Given a polygonal approximation $\Omega_h$ of the domain $\Omega$, the standard order $m$ VEM [@hitchVEM], for $m$ increasing, leads to a suboptimal convergence rate. We adapt the approach of [@BDT] to VEM and we prove that an optimal convergence rate can be achieved by using a suitable correction depending on high order normal derivatives of the discrete solution at the boundary edges of $\Omega_h$, which, to retain computability, is evaluated after applying the projector $\Pi^\nabla$ onto the space of polynomials. Numerical experiments confirm the theory.'
address:
- 'IMATI “E. Magenes”, CNR, Pavia (Italy)'
- 'IMATI “E. Magenes”, CNR, Pavia (Italy)'
- 'IMATI “E. Magenes”, CNR, Pavia (Italy)'
author:
- Silvia Bertoluzza
- Micol Pennacchio
- Daniele Prada
title: 'High order VEM on curved domains.'
---

[10]{}

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