Embedded Trefftz DG method for the Helmholtz equation
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910051875160064 |
|---|---|
| author | Stocker, Paul Voulis, Igor |
| author_facet | Stocker, Paul Voulis, Igor |
| contents | We study an embedded Trefftz discontinuous Galerkin method for the Helmholtz equation. The method starts from a polynomial DG space and enforces the Trefftz property through local constraints, avoiding an explicit construction of Trefftz basis functions. For the global coupling we use a simple symmetric interior penalty DG bilinear form. Since the resulting formulation is not coercive, stability is proved by a $T$-coercivity argument combined with a Schatz-type duality technique. This yields wavenumber-explicit stability, quasi-optimality, and convergence estimates in standard DG norms under an explicit mesh resolution condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13034 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Embedded Trefftz DG method for the Helmholtz equation Stocker, Paul Voulis, Igor Numerical Analysis 65N30, 65N15, 65N12, 35J05 We study an embedded Trefftz discontinuous Galerkin method for the Helmholtz equation. The method starts from a polynomial DG space and enforces the Trefftz property through local constraints, avoiding an explicit construction of Trefftz basis functions. For the global coupling we use a simple symmetric interior penalty DG bilinear form. Since the resulting formulation is not coercive, stability is proved by a $T$-coercivity argument combined with a Schatz-type duality technique. This yields wavenumber-explicit stability, quasi-optimality, and convergence estimates in standard DG norms under an explicit mesh resolution condition. |
| title | Embedded Trefftz DG method for the Helmholtz equation |
| topic | Numerical Analysis 65N30, 65N15, 65N12, 35J05 |
| url | https://arxiv.org/abs/2603.13034 |