Stabilizer-free polygonal and polyhedral virtual elements

09/19/2023

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by   Yanping Lin, et al.

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Stabilizer-free P_k virtual elements are constructed on polygonal and polyhedral meshes. Here the interpolating space is the space of continuous P_k polynomials on a triangular-subdivision of each polygon, or a tetrahedral-subdivision of each polyhedron. With such an accurate and proper interpolation, the stabilizer of the virtual elements is eliminated while the system is kept positive-definite. We show that the stabilizer-free virtual elements converge at the optimal order in 2D and 3D. Numerical examples are computed, validating the theory.