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This paper presents a simplified weak Galerkin (WG) finite element method for solving biharmonic equations avoiding the use of traditional stabilizers. The proposed WG method supports both convex and non-convex polytopal elements in finite element partitions, utilizing bubble functions as a critical analytical tool. The simplified WG method is symmetric and positive definite. Optimal-order error estimates are established for WG approximations in both the discrete \(H^2\) norm and the \(L^2\) norm.

Details

1009240
Subject
Finite element method;
Error analysis;
Biharmonic equations;
Galerkin method
Identifier / keyword
Numerical Analysis
URL
http://arxiv.org/abs/2412.11315
Title
Simplified Weak Galerkin Finite Element Methods for Biharmonic Equations on Non-Convex Polytopal Meshes
Author
Wang, Chunmei
Publication title
arXiv.org; Ithaca
Publication year
2024
Publication date
Dec 15, 2024
Section
Computer Science; Mathematics
Publisher
Cornell University Library, arXiv.org
Source
arXiv.org
Place of publication
Ithaca
Country of publication
United States
University/institution
Cornell University Library arXiv.org
Publication subject
Biology, Statistics, Physics, Mathematics, Engineering--Electrical Engineering, Computers--Computer Engineering, Business And Economics--Banking And Finance
e-ISSN
2331-8422
Source type
Working Paper
Language of publication
English
Document type
Working Paper
Publication history
 
 
Online publication date
2024-12-17
Milestone dates
2024-12-15 (Submission v1)
Publication history
 
 
   First posting date
17 Dec 2024
ProQuest document ID
3145906630
Document URL
https://www.proquest.com/working-papers/simplified-weak-galerkin-finite-element-methods/docview/3145906630/se-2?accountid=208611
Full text outside of ProQuest
http://arxiv.org/abs/2412.11315
Copyright
© 2024. This work is published under http://creativecommons.org/publicdomain/zero/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Last updated
2024-12-18
Database
2 databases
  • ProQuest One Academic
  • ProQuest One Academic