Enhancing least-squares finite element methods through a quantity-of-interest

Jehanzeb Hameed Chaudhry, Eric C. Cyr, Kuo Liu, Thomas A. Manteuffel, Luke N. Olson, Lei Tang

Research output: Contribution to journalArticle

Abstract

In this paper we introduce an approach that augments least-squares finite element formulations with user-specified quantities-of-interest. The method incorporates the quantity-ofinterest into the least-squares functional and inherits the global approximation properties of the standard formulation as well as increased resolution of the quantity-of-interest. We establish theoretical properties such as optimality and enhanced convergence under a set of general assumptions. Central to the approach is that it offers an element-level estimate of the error in the quantity-ofinterest. As a result, we introduce an adaptive approach that yields efficient, adaptively refined approximations. Several numerical experiments for a range of situations are presented to support the theory and highlight the effectiveness of our methodology. Notably, the results show that the new approach is effective at improving the accuracy per total computational cost.

Original languageEnglish (US)
Pages (from-to)3085-3105
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume52
Issue number6
DOIs
StatePublished - Jan 1 2014

Keywords

  • Adaptive mesh refinement
  • Error estimation
  • Finite element
  • Least-squares

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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