Exponential convergence in H$^{1}$ of hp-FEM for Gevrey regularity with isotropic singularities
Abstract:
For functions u∈H$^{1}$(Ω) in a bounded polytope Ω⊂R$^{d}$, d=1,2,3 which are Gevrey regular in Ω¯¯¯¯∖S with point singularities concentrated at a set S⊂Ω¯¯¯¯ consisting of a finite number of points in Ω¯¯¯¯, we prove exponential rates of convergence of hp-version continuous Galerkin finite element methods on families of regular, simplicial meshes in Ω. The simplicial meshes are geometrically refined towards S but are otherwise unstructured.
| Zugehörige Institution(en) am KIT | Institut für Angewandte und Numerische Mathematik (IANM) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsjahr | 2018 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X urn:nbn:de:swb:90-869097 KITopen-ID: 1000086909 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 22 S. |
| Serie | CRC 1173 ; 2018/23 |