Convergence and optimality of adaptive least squares finite element methods

Carsten Carstensen, Eun-Jae Park

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The first-order div least squares finite element methods (LSFEMs) allow for an immediate a posteriori error control by the computable residual of the least squares functional. This paper establishes an adaptive refinement strategy based on some equivalent refinement indicators. Since the first-order div LSFEM measures the flux errors in H (div), the data resolution error measures the L 2 norm of the right-hand side f minus the piecewise polynomial approximation II f without a mesh-size factor. Hence the data resolution term is neither an oscillation nor of higher order and consequently requires a particular treatment, e.g., by the thresholding second algorithm due to Binev and DeVore. The resulting novel adaptive LSFEM with separate marking converges with optimal rates relative to the notion of a nonlinear approximation class.

Original languageEnglish
Pages (from-to)43-62
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume53
Issue number1
DOIs
Publication statusPublished - 2014 Jan 1

Fingerprint

Least-squares Finite Element Method
Optimality
Finite element method
First-order
Adaptive Refinement
Polynomial approximation
Nonlinear Approximation
Optimal Rates
Piecewise Polynomials
Error Control
Polynomial Approximation
Thresholding
Least Squares
Refinement
Mesh
Oscillation
Higher Order
Fluxes
Converge
Norm

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Convergence and optimality of adaptive least squares finite element methods. / Carstensen, Carsten; Park, Eun-Jae.

In: SIAM Journal on Numerical Analysis, Vol. 53, No. 1, 01.01.2014, p. 43-62.

Research output: Contribution to journalArticle

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