Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems

Alex Bespalov, Alexander Haberl, Dirk Praetorius

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)
145 Downloads (Pure)

Abstract

We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Gårding inequality, adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence with optimal algebraic rates. As an important consequence of our analysis, one does not have to deal with the a priori assumption that the underlying meshes are sufficiently fine. Hence, the overall conclusion of our results is that adaptivity has stabilizing effects and can overcome possibly pessimistic restrictions on the meshes. In particular, our analysis covers adaptive mesh-refinement for the finite element discretization of the Helmholtz equation from where our interest originated.
Original languageEnglish
Pages (from-to)318-340
Number of pages23
JournalComputer Methods in Applied Mechanics and Engineering
Volume317
Early online date19 Dec 2016
DOIs
Publication statusPublished - 15 Apr 2017

Keywords

  • Adaptive mesh-refinement
  • Optimal convergence rates
  • a posteriori error estimate
  • Helmholtz equation

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