Nonconforming Virtual Element Method for $2m$th Order Partial Differential Equations in $\mathbb {R}^n$

A unified construction of the H^mnonconforming virtual elements of any order kis developed on any shape of polytope in \mathbb {R}^nwith constraints m\leq nand k\geq m As a vital tool in the construction, a generalized Green’s identity for H^minner product is derived. The H^mnonconforming virtual element methods are then used to approximate solutions of the mharmonic equation. After establishing a bound on the jump...