Numerical analysis reveals improved accuracy using L2 projection and convergence assessment in 3D models.
Abstract In this paper, we describe the 3D Nonconforming Virtual Element Method, where the local spaces are enhanced in order to build an L² projection of virtual functions onto polynomials of degree k. This higher order projection provides a more accurate representation of the load term and, more importantly, it enables the construction of the reaction term. We conduct a convergence analysis of the L² norm and H¹ seminorm errors with respect to mesh size and approximation degree. We also compare our results with those obtained using the conforming Virtual Element Method.
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Trezzi et al. (2025) studied this question.
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