Convergence of natural adaptive least squares finite element methods

Carsten Carstensen, Eun Jae Park, Philipp Bringmann

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The first-order div least squares finite element methods provide inherent a posteriori error estimator by the elementwise evaluation of the functional. In this paper we prove Q-linear convergence of the associated adaptive mesh-refining strategy for a sufficiently fine initial mesh with some sufficiently large bulk parameter for piecewise constant right-hand sides in a Poisson model problem. The proof relies on some modification of known supercloseness results to non-convex polygonal domains plus the flux representation formula. The analysis is carried out for the lowest-order case in two-dimensions for the simplicity of the presentation.

Original languageEnglish
Pages (from-to)1097-1115
Number of pages19
JournalNumerische Mathematik
Volume136
Issue number4
DOIs
Publication statusPublished - 2017 Aug 1

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Least-squares Finite Element Method
Linear Convergence
Adaptive Mesh
A Posteriori Error Estimators
Representation Formula
Poisson Model
Refining
Lowest
Simplicity
Two Dimensions
Mesh
Fluxes
First-order
Finite element method
Evaluation
Strategy
Presentation

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

Carstensen, Carsten ; Park, Eun Jae ; Bringmann, Philipp. / Convergence of natural adaptive least squares finite element methods. In: Numerische Mathematik. 2017 ; Vol. 136, No. 4. pp. 1097-1115.
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Convergence of natural adaptive least squares finite element methods. / Carstensen, Carsten; Park, Eun Jae; Bringmann, Philipp.

In: Numerische Mathematik, Vol. 136, No. 4, 01.08.2017, p. 1097-1115.

Research output: Contribution to journalArticle

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