Stabilization-Free Virtual Element Methods

12/04/2022
by   Chunyu Chen, et al.
0

Stabilization-free virtual element methods in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming virtual element method in arbitrary dimension and a conforming virtual element method in two dimensions. The key is to construct local H(div)-conforming macro finite element spaces such that the associated L^2 projection of the gradient of virtual element functions is computable, and the L^2 projector has a uniform lower bound on the gradient of virtual element function spaces in L^2 norm. Optimal error estimates are derived for these stabilization-free virtual element methods. Numerical results are provided to verify the convergence rates.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset