Abstract

The aim of this work is to analyze virtual element methods to solve the Oseen equations in terms of the stream-function on simply connected polygonal domains. The methods are based on a C1-conforming discretization of arbitrary order k ≥ 2. Under standard assumptions on the computational domain, we establish that the resulting schemes converge with an optimal order in H2(Ω). The proposed methods have the advantages of using general polygonal meshes and the possibility to compute further variables of interest, such as the velocity, the vorticity and the pressure. Finally, we report some numerical test illustrating the behavior of the virtual schemes and supporting our theoretical results on different families of polygonal meshes.