Equivalence of Weak Galerkin Methods and Virtual Element Methods for Elliptic Equations
Theoretical unification for numerical analysts working on finite element methods for elliptic PDEs.
The paper establishes equivalence between modified weak Galerkin methods and a new version of virtual element methods for elliptic equations, and between the original weak Galerkin method and non-conforming virtual element methods, enabling transfer of ideas between the two approaches.
We propose a modification of the weak Galerkin methods and show its equivalence to a new version of virtual element methods. We also show the original weak Galerkin method is equivalent to the non-conforming virtual element method. As a consequence, ideas and techniques used for one method can be transferred to another. The key of the connection is the degree of freedoms.