DeepAI AI Chat
Log In Sign Up

On the maximum angle conditions for polyhedra with virtual element methods

12/14/2022
by   Ruchi Guo, et al.
0

Finite element methods are well-known to admit robust optimal convergence on simplicial meshes satisfying the maximum angle conditions. But how to generalize this condition to polyhedra is unknown in the literature. In this work, we argue that this generation is possible for virtual element methods (VEMs). In particular, we develop an anisotropic analysis framework for VEMs where the virtual spaces and projection spaces remain abstract and can be problem-adapted, carrying forward the “virtual” spirit of VEMs. Three anisotropic cases will be analyzed under this framework: (1) elements only contain non-shrinking inscribed balls but are not necessarily star convex to those balls; (2) elements are cut arbitrarily from a background Cartesian mesh, which can extremely shrink; (3) elements contain different materials on which the virtual spaces involve discontinuous coefficients. The error estimates are guaranteed to be independent of polyhedral element shapes. The present work largely improves the current theoretical results in the literature and also broadens the scope of the application of VEMs.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/08/2021

A Virtual Finite Element Method for Two Dimensional Maxwell Interface Problems with a Background Unfitted Mesh

A virtual element method (VEM) with the first order optimal convergence ...
08/02/2021

Immersed Virtual Element Methods for Elliptic Interface Problems

This article presents an immersed virtual element method for solving a c...
02/21/2022

Immersed Virtual Element Methods for Maxwell Interface Problems in Three Dimensions

Finite element methods for Maxwell's equations are highly sensitive to t...
05/25/2021

Optimal maximum norm estimates for virtual element methods

The maximum norm error estimations for virtual element methods are studi...
05/22/2020

Staggered DG method with small edges for Darcy flows in fractured porous media

In this paper, we present and analyze a staggered discontinuous Galerkin...
05/24/2022

Construction and analysis of the quadratic finite volume methods on tetrahedral meshes

A family of quadratic finite volume method (FVM) schemes are constructed...
12/02/2020

SUPG-stabilized Virtual Elements for diffusion-convection problems: a robustness analysis

The objective of this contribution is to develop a convergence analysis ...