The Mixed Virtual Element Method on curved edges in two dimensions

Abstract

In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical feature, such as a portion of domain boundary or an internal interface, may introduce a geometrical error that degrades the expected order of convergence of the scheme. In the present work a suitable VEM approximation space is proposed to consistently handle curvilinear geometrical objects, thus recovering optimal convergence rates. The resulting numerical scheme is presented along with its theoretical analysis and several numerical test cases to validate the proposed approach.

References in corpus (4)

• An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincaré inequalities, and consistency
• Virtual Elements and curved edges
• Interpolation and stability properties of low order face and edge virtual element spaces
• Adaptive virtual element methods with equilibrated fluxes

Cited by in corpus (4)

• Immersed Virtual Element Methods for Electromagnetic Interface Problems in Three Dimensions
• Orthogonal polynomial bases in the Mixed Virtual Element Method
• Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media
• Bend 3d Mixed Virtual Element Method for Elliptic Problems