Two-level Additive Schwarz Algorithm For Solving Second-order Elliptic Problems With Incongruent Dummy Element Methods

In this paper,we propose a two level additive Schwarz preconditioner for the nonconforming virtual element discretization of the second order elliptic problems.The nonconforming virtual element method is a discrete method based on polygonal meshes,which can be more suitable to deal with problems in more complex regions.Since the coarse mesh and fine mesh spaces are non-nested,and bilinear forms are non-inheritance.We construct a type of transfer operator between the coarse mesh and fine mesh spaces by using the conforming virtual element as a bridge.The stability and approximation of the operators are proved by using the local of Galerkin projection.Under the framework of the two level additive Schwarz algorithm,it is proved that the condition number of the preconditioned system is OO(1+(H/?~2),where H denotes the size of the coarse mesh and ? denotes the size of the overlapping.Numerical experiments verify the theoretical results.