On Adaptive Eulerian–Lagrangian Method for Linear Convection–Diffusion Problems View Full Text


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Article Info

DATE

2014-01

AUTHORS

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

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. More... »

PAGES

90-114

References to SciGraph publications

  • 2004-04. Adaptive Finite Element Methods with convergence rates in NUMERISCHE MATHEMATIK
  • 2009. Theory of adaptive finite element methods: An introduction in MULTISCALE, NONLINEAR AND ADAPTIVE APPROXIMATION
  • 2004-01. Adaptive computation for convection dominated diffusion problems in SCIENCE IN CHINA SERIES A MATHEMATICS
  • 1982-10. On the transport-diffusion algorithm and its applications to the Navier-Stokes equations in NUMERISCHE MATHEMATIK
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10915-013-9731-y

    DOI

    http://dx.doi.org/10.1007/s10915-013-9731-y

    DIMENSIONS

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