
H^mConforming Virtual Elements in Arbitrary Dimension
The H^mconforming virtual elements of any degree k on any shape of poly...
read it

Optimal maximum norm estimates for virtual element methods
The maximum norm error estimations for virtual element methods are studi...
read it

An enhanced VEM formulation for plane elasticity
In this paper, an enhanced Virtual Element Method (VEM) formulation is p...
read it

A general approach for constructing robust virtual element methods for fourth order problems
We present a class of nonconforming virtual element methods for general ...
read it

Piecewise DivergenceFree H(div)Nonconforming Virtual Elements for Stokes Problem in Any Dimensions
Piecewise divergencefree H(div)nonconforming virtual elements are desi...
read it

Mixed virtual volume methods for elliptic problems
We develop a class of mixed virtual volume methods for elliptic problems...
read it

Additive Schwarz methods for serendipity elements
While solving Partial Differential Equations (PDEs) with finite element ...
read it
Nonconforming Virtual Element Method for 2mth Order Partial Differential Equations in R^n with m>n
The H^mnonconforming virtual elements of any order k on any shape of polytope in R^n with constraints m> n and k≥ m are constructed in a universal way. A generalized Green's identity for H^m inner product m>n is derived, which is essential to devise the H^mnonconforming virtual elements. The dimension of the H^mnonconforming virtual elements can reduced by the Serendipity approach. By means of the local H^m projection and a stabilization term using the boundary degrees of freedom, the H^mnonconforming virtual element methods are proposed to approximate solutions of the mharmonic equation. The norm equivalence of the stabilization on the kernel of the local H^m projection is proved by using the bubble function technique, the Poincaré inquality and the trace inequality, which implies the wellposedness of the virtual element methods. Finally, the optimal error estimates for the H^mnonconforming virtual element methods are achieved from an estimate of the weak continuity and the error estimate of the canonical interpolation.
READ FULL TEXT
Comments
There are no comments yet.