On adaptive Eulerian-Lagrangian method for linear convection-diffusion problems

Xiaozhe Hu, Young Ju Lee, Jinchao Xu, Chen Song Zhang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this paper, we consider the adaptive Eulerian-Lagrangian method (ELM) for linear convection-diffusion problems. Unlike classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a new a posteriori error bound for ELM semi-discretization. With the help of this proposed error bound, we are able to show the optimal convergence rate of ELM for solutions with minimal regularity. Furthermore, by combining this error bound with a standard residual-type estimator for the spatial error, we obtain a posteriori error estimators for a fully discrete scheme. We present numerical tests to demonstrate the efficiency and robustness of our adaptive algorithm.

Original languageEnglish (US)
Pages (from-to)90-114
Number of pages25
JournalJournal of Scientific Computing
Volume58
Issue number1
DOIs
StatePublished - Jan 2014

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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