Simplified Weak Galerkin Finite Element Methods for Biharmonic Equations on Non-Convex Polytopal Meshes
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915065377062912 |
|---|---|
| author | Wang, Chunmei |
| author_facet | Wang, Chunmei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simplified Weak Galerkin Finite Element Methods for Biharmonic Equations on Non-Convex Polytopal Meshes Wang, Chunmei Numerical Analysis 65N30, 65N15, 65N12, 65N20 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. |
| title | Simplified Weak Galerkin Finite Element Methods for Biharmonic Equations on Non-Convex Polytopal Meshes |
| topic | Numerical Analysis 65N30, 65N15, 65N12, 65N20 |
| url | https://arxiv.org/abs/2412.11315 |