Optimal maximum norm estimates of virtual element methods for elliptic problem in three dimensions

Wenming He; Ren Zhao

doi:10.1016/j.camwa.2025.08.011

Optimal maximum norm estimates of virtual element methods for elliptic problem in three dimensions

Wenming He, Ren Zhao

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we derive the optimal maximum norm estimates for virtual element methods for elliptic problems in three dimensions under suitable local smoothness assumption of the solution. Finally, numerical examples are used to investigate our main results on tetrahedral and polyhedral meshes.

Original language	English
Pages (from-to)	167-182
Number of pages	16
Journal	Computers and Mathematics with Applications
Volume	197
DOIs	https://doi.org/10.1016/j.camwa.2025.08.011
Publication status	Published - 1 Nov 2025

Keywords

Elliptic problems
Maximum norm estimates
Virtual element methods

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10.1016/j.camwa.2025.08.011

Cite this

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title = "Optimal maximum norm estimates of virtual element methods for elliptic problem in three dimensions",

abstract = "In this article, we derive the optimal maximum norm estimates for virtual element methods for elliptic problems in three dimensions under suitable local smoothness assumption of the solution. Finally, numerical examples are used to investigate our main results on tetrahedral and polyhedral meshes.",

keywords = "Elliptic problems, Maximum norm estimates, Virtual element methods",

author = "Wenming He and Ren Zhao",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Ltd",

year = "2025",

month = nov,

day = "1",

doi = "10.1016/j.camwa.2025.08.011",

language = "English",

volume = "197",

pages = "167--182",

journal = "Computers and Mathematics with Applications",

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T1 - Optimal maximum norm estimates of virtual element methods for elliptic problem in three dimensions

AU - He, Wenming

AU - Zhao, Ren

PY - 2025/11/1

Y1 - 2025/11/1

N2 - In this article, we derive the optimal maximum norm estimates for virtual element methods for elliptic problems in three dimensions under suitable local smoothness assumption of the solution. Finally, numerical examples are used to investigate our main results on tetrahedral and polyhedral meshes.

AB - In this article, we derive the optimal maximum norm estimates for virtual element methods for elliptic problems in three dimensions under suitable local smoothness assumption of the solution. Finally, numerical examples are used to investigate our main results on tetrahedral and polyhedral meshes.

KW - Elliptic problems

KW - Maximum norm estimates

KW - Virtual element methods

UR - https://www.scopus.com/pages/publications/105013964609

U2 - 10.1016/j.camwa.2025.08.011

DO - 10.1016/j.camwa.2025.08.011

M3 - Article

AN - SCOPUS:105013964609

SN - 0898-1221

VL - 197

SP - 167

EP - 182

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

ER -

Optimal maximum norm estimates of virtual element methods for elliptic problem in three dimensions

Abstract

Keywords

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Frontier Research on high accuracy numerical methods for plasma simulation

High accuracy particle in cell method for plasma simulation

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Optimal maximum norm estimates of virtual element methods for elliptic problem in three dimensions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Frontier Research on high accuracy numerical methods for plasma simulation

High accuracy particle in cell method for plasma simulation

Cite this