VEM Ansatz Functions and Projection for the Poisson Equation

The formulation of virtual elements for heat conduction problems, see ( 2.42 ), or more general for the Poisson equation ( \(-\Delta \,\theta = f\) ) was one of the starting points of this method, see Beirão da Veiga et al. (2013) and Beirão da Veiga et al. (2014). Since Laplace, Poisson and the elasticity equations are of elliptical nature, the ansatz functions defined in the previous chapter can be employed for these scalar valued problems as well.