Construction of the Virtual Element

So far we have formulated ways to compute the projection of an ansatz function \(\boldsymbol{u}_h\) onto a polynomial space \(\boldsymbol{u}_\pi \) for the virtual element method using a linear or a quadratic order interpolation. These projections provide the basis for the discretization of linear and nonlinear partial differential equations related to the Poisson equations and many applications in solid mechanics. Once the approximate field is known its gradients can be computed and with this all equations can be discretized using the ansatz functions derived in Chap.  3 for solids and in Chap.  4 for the Poisson equation.