JournalsrlmVol. 30, No. 2pp. 391–412

High order VEM on curved domains

  • Silvia Bertoluzza

    Università di Pavia, Italy
  • Micol Pennacchio

    Università di Pavia, Italy
  • Daniele Prada

    Università di Pavia, Italy
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Abstract

We deal with the virtual element method (VEM) for solving the Poisson equation on a domain Ω\Omega with curved boundary. Given a polygonal approximation Ωh\Omega_h of the domain Ω\Omega, the standard order mm VEM [6], for mm increasing, leads to a suboptimal convergence rate. We adapt the approach of [14] 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 Ωh\Omega_h, which, to retain computability, is evaluated after applying the projector Π\Pi^{\nabla} onto the space of polynomials. Numerical experiments confirm the theory.

Cite this article

Silvia Bertoluzza, Micol Pennacchio, Daniele Prada, High order VEM on curved domains. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 2, pp. 391–412

DOI 10.4171/RLM/853