Basic principles of hp virtual elements on quasiuniform meshes

Abstract

In the present paper we initiate the study of [Formula: see text] Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size [Formula: see text] and in the polynomial degree [Formula: see text] in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included.