Nonconforming virtual element method for 2mth order partial differential equations in Rn with m > n
Nonconforming virtual element method for 2mth order partial differential equations in Rn with m > n
复制标题
Rn 中 m > n 的 2m 阶偏微分方程的非协调虚元法
DOI：
10.1007/s10092-020-00381-7
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发表时间：
2020
期刊：
影响因子：
1.7
通讯作者：
Huang Xuehai
中科院分区：
文献类型：
--
作者：
Huang Xuehai
The $$H^m$$ H m -nonconforming virtual elements of any orderkon any shape of polytope in $${\mathbb {R}}^n$$ R n with constraints $$m> n$$ m > n and $$k\ge m$$ k ≥ m are constructed in a universal way. A generalized Green’s identity for $$H^m$$ H m inner product with $$m>n$$ m > n is derived, which is essential to devise the $$H^m$$ H m -nonconforming virtual elements. By means of the local $$H^m$$ H m projection and a stabilization term using only the boundary degrees of freedom, the $$H^m$$ H m -nonconforming virtual element methods are proposed to approximate solutions of them-harmonic equation. The norm equivalence of the stabilization on the kernel of the local $$H^m$$ H m projection is proved by using the bubble function technique, the Poincaré inquality and the trace inequality, which implies the well-posedness of the virtual element methods. The optimal error estimates for the $$H^m$$ H m -nonconforming virtual element methods are achieved from an estimate of the weak continuity and the error estimate of the canonical interpolation. Finally, the implementation of the nonconforming virtual element method is discussed.
