High order VEM on curved domains [1]

<p>We deal with the virtual element method (VEM) for solving the Poisson equation on a domain Ω with curved boundaries. Given a polygonal approximation Ωh of the domain Ω, the standard order m VEM [6], for m 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, which, to retain computability, is evaluated after applying the projector Π∇ onto the space of polynomials. Numerical experiments confirm the theory.</p>