Stabilizer-free polygonal and polyhedral virtual elements

2023/09/19 by Lin, Yanping, Mu, Mo, Zhang, Shangyou
#65N15 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2309.10250

Abstract

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.

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