• Media type: Text; Report; E-Book
  • Title: Optimal W$^{1,∞}$-estimates for an isoparametric finite element discretization of elliptic boundary value problems
  • Contributor: Dörich, Benjamin [Author]; Leibold, Jan [Author]; Maier, Bernhard [Author]
  • imprint: Karlsruher Institut für Technologie, 2022-02-08
  • Language: English
  • DOI: https://doi.org/10.5445/IR/1000142881/v2
  • ISSN: 2365-662X
  • Keywords: maximum norm error estimates ; nonconforming space discretization ; isoparametric finite elements ; Mathematics ; Ritz map ; elliptic boundary value problem ; weighted norms ; a-priori error estimates
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  • Description: In this paper, we consider an elliptic boundary value problem on a domain with regular boundary and discretize it with isoparametric finite elements of order $k\geq1$. We show optimal order of convergence of the isoparametric finite element solution in the $W^{1,\infty}$-norm. As an intermediate step, we derive stability and convergence estimates of optimal order $k$ for a (generalized) Ritz map.
  • Access State: Open Access