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.

翻译：在多边形与多面体网格上构建了无稳定项$P_k$虚拟元。其中插值空间定义为每个多边形三角剖分或多面体四面体剖分上的连续$P_k$多项式空间。借助这种精确且恰当的插值方法，既消除了虚拟元的稳定项，又保持了系统的正定性。我们证明无稳定项虚拟元在二维和三维空间中均能达到最优收敛阶。通过数值算例验证了理论分析的正确性。