Anisotropic Error Estimates of The Linear Nonconforming Virtual Element Methods

Abstract

A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape regularity of polytopal meshes. A new error equation for the lowest order (linear) nonconforming VEM is derived for any choice of stabilization, and a new stabilization using a projection on an extended element patch is introduced for the error analysis on anisotropic elements.

References in corpus (5)

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• Analysis of Compatible Discrete Operator Schemes for Elliptic Problems on Polyhedral Meshes
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• Anisotropic Error Estimates of The Linear Virtual Element Method on Polygonal Meshes
• High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations

Cited by in corpus (7)

• Immersed Virtual Element Methods for Electromagnetic Interface Problems in Three Dimensions
• A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects
• Immersed Virtual Element Methods for Elliptic Interface Problems in Two Dimensions
• Nonconforming Virtual Element Method for $2m$-th Order Partial Differential Equations in ${\mathbb{R}}^n$
• Anisotropic a posteriori error estimate for the Virtual Element Method
• A simple virtual element-based flux recovery on quadtree
• The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation