A Least-Squares Weak Galerkin Finite Element Scheme for Cauchy Problems in Helmholtz
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910240798146560 |
|---|---|
| author | Wang, Chunmei Zhang, Shangyou |
| author_facet | Wang, Chunmei Zhang, Shangyou |
| contents | This paper introduces and rigorously analyzes a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem associated with the Helmholtz equation. By utilizing a weak Laplacian operator defined on a space of discontinuous functions, the proposed framework facilitates the seamless treatment of complex boundary conditions and internal interfaces. We emphasize the geometric flexibility of the LS-WG scheme on general polygonal and polyhedral partitions. Furthermore, we prove the uniqueness of the numerical solution and derive optimal-order error estimates with respect to a specifically designed discrete energy norm. Extensive numerical experiments validate the theoretical convergence rates and demonstrate the algorithm's robustness and efficiency over traditional Galerkin approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21162 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Least-Squares Weak Galerkin Finite Element Scheme for Cauchy Problems in Helmholtz Wang, Chunmei Zhang, Shangyou Numerical Analysis This paper introduces and rigorously analyzes a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem associated with the Helmholtz equation. By utilizing a weak Laplacian operator defined on a space of discontinuous functions, the proposed framework facilitates the seamless treatment of complex boundary conditions and internal interfaces. We emphasize the geometric flexibility of the LS-WG scheme on general polygonal and polyhedral partitions. Furthermore, we prove the uniqueness of the numerical solution and derive optimal-order error estimates with respect to a specifically designed discrete energy norm. Extensive numerical experiments validate the theoretical convergence rates and demonstrate the algorithm's robustness and efficiency over traditional Galerkin approaches. |
| title | A Least-Squares Weak Galerkin Finite Element Scheme for Cauchy Problems in Helmholtz |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.21162 |