Log In Sign Up

Optimal maximum norm estimates for virtual element methods

by   Wen-Ming He, et al.

The maximum norm error estimations for virtual element methods are studied. To establish the error estimations, we prove higher local regularity based on delicate analysis of Green's functions and high-order local error estimations for the partition of the virtual element solutions. The maximum norm of the exact gradient and the gradient of the projection of the virtual element solutions are proved to achieve optimal convergence results. For high-order virtual element methods, we establish the optimal convergence results in L^∞ norm. Our theoretical discoveries are validated by a numerical example on general polygonal meshes.


page 1

page 2

page 3

page 4


Stabilization-Free Virtual Element Methods

Stabilization-free virtual element methods in arbitrary degree of polyno...

The virtual element method for linear elastodynamics models. Design, analysis, and implementation

We design the conforming virtual element method for the numerical simula...

Nonconforming Virtual Element Method for 2m-th Order Partial Differential Equations in R^n with m>n

The H^m-nonconforming virtual elements of any order k on any shape of po...

Two types of spectral volume methods for 1-D linear hyperbolic equations with degenerate variable coefficients

In this paper, we analyze two classes of spectral volume (SV) methods fo...

A general approach for constructing robust virtual element methods for fourth order problems

We present a class of nonconforming virtual element methods for general ...

A posteriori virtual element method for the acoustic vibration problem

In two dimensions, we propose and analyze an a posteriori error estimato...

On the maximum angle conditions for polyhedra with virtual element methods

Finite element methods are well-known to admit robust optimal convergenc...