On the Implementation of Virtual Element Method for Nonlinear Problems over Polygonal Meshes

We present the details of the implementation of the Virtual Element Method (VEM) for nonlinear elliptic and parabolic problems, over polygonal meshes. The VEM implementation of a nonlinear problem does not follow the traditional way of implementation of the nonlinear problems as done in finite element/finite volume or finite difference methods. To facilitate this, suitable projection operators are used for the nonlinear terms that are rewritten in terms of the degrees of freedom associated with the virtual element space and thus are computable. We explicitly present the discretization and include sample codes that will help readers with the basic implementation of the nonlinear problems.