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Stabilizer-free polygonal and polyhedral virtual elements

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arxiv 2309.10250 v1 pith:Y6AIMAL2 submitted 2023-09-19 math.NA cs.NA

Yanping Lin , Mo Mu , Shangyou Zhang This is my paper · ORCID
classification math.NAcs.NA
keywords elementsvirtualstabilizer-freepolygonalpolyhedralspaceaccuratecomputed
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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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