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We propose a modification of the weak Galerkin methods and show itsequivalence to a new version of virtual element methods. We also show theoriginal weak Galerkin method is equivalent to the non-conforming virtualelement method. As a consequence, ideas and techniques used for one method canbe transferred to another. The key of the connection is the degree of freedoms.

Equivalence of Weak Galerkin Methods and Virtual Element Methods for Elliptic Equations