  In this paper, we employ the linear virtual element spaces to discretize the
semilinear sine-Gordon equation in two dimensions. The salient features of the
virtual element method (VEM) are: (a) it does not require explicit form of the
shape functions to construct the nonlinear and the bilinear terms, and (b)
relaxes the constraint on the mesh topology by allowing the domain to be
discretized with general polygons consisting of both convex and concave
elements, and (c) easy mesh refinements (hanging nodes and interfaces are
allowed). The nonlinear source term is discretized by employing the product
approximation technique and for temporal discretization, the Crank-Nicolson
scheme is used. The resulting nonlinear equations are solved using the Newton's
method. We derive a priori error estimations in $L^2$ and $H^1$ norms. The
convergence properties and the accuracy of the virtual element method for the
solution of the sine-Gordon equation are demonstrated with academic numerical
experiments.
