A High-Order Shifted Boundary Virtual Element Method for Poisson Equations on 2D Curved Domains

We consider a high-order virtual element method for Poisson problems with non-homogeneous Dirichlet boundary condition on 2D domains with curved boundary. The scheme is designed on unfitted polygonal meshes. It borrows the idea of the shifted boundary method proposed by Main and Scovazzi (J Comput Phys 372:972–995, 2018) for treating the curved boundary. We prove the stability and the optimal error estimate in energy norm for the proposed method. For the \(L^2\) $L^2$ norm, although suboptimal error estimate is proved theoretically, numerical results appear to be optimal. Supporting numerical results are presented.