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 method is verified for different polygonal partitions. An specific mesh-free application that allows to approximate harmonic functions is discussed, based on high-order projections. This approach significantly improves running times compared to usual finite or virtual element methods, and can be modified for different virtual spaces and elliptic partial differential equations.

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