A numerical implementation for the high-order 2D virtual element method in MATLAB

We present a numerical implementation for the Virtual Element Method that incorporates high order spaces. We include all the required computations in order to assemble the stiffness and mass matrices, and right hand side. Convergence of the method is verified for different polygonal partitions. An specific mesh-free application that allows to approximate harmonic functions is discussed, which is based on high-order projections onto polynomial spaces of degree k; this approach only requires to solve a k(k - 1)/2 linear system, reducing significantly the number of operations compared to usual finite or virtual element methods, and can be modified for different virtual spaces and elliptic partial differential equations.