Research reports

Exponential convergence in H 1 of hp-FEM for Gevrey regularity with isotropic singularities

by M. Feischl and Ch. Schwab

(Report number 2018-29)

Abstract
For functions \(u\in H^1(\Omega)\) in a bounded polytope \(\Omega\subset {\mathbb R}^d\), \(d=1,2,3\) which are Gevrey regular in \(\overline{\Omega}\backslash {\mathcal S}\) with point singularities concentrated at a set \({\mathcal S}\subset \overline{\Omega}\) consisting of a finite number of points in \(\overline{\Omega}\), we prove exponential rates of convergence of \(hp\)-version continuous Galerkin finite element methods on families of regular, simplicial meshes in \(\Omega\). The simplicial meshes are geometrically refined towards \({\mathcal S}\) but are otherwise unstructured.

Keywords:

BibTeX
@Techreport{FS18_783,
  author = {M. Feischl and Ch. Schwab},
  title = {Exponential convergence in H 1 of hp-FEM for Gevrey regularity with isotropic singularities},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-29},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-29.pdf },
  year = {2018}
}

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