Chunyu Chen, Xuehai Huang, Huayi Wei
Published 2022-12-04Version 1
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 $H(\textrm{div})$-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.
The nonconforming virtual element method
Nonconforming Virtual Element Method for $2m$-th Order Partial Differential Equations in $\mathbb R^n$ with $m>n$
Nonconforming Virtual Element Method for $2m$-th Order Partial Differential Equations in $\mathbb R^n$
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