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Comparison of two-dimensional r-adaptive finite element methods using various error indicators

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  • Cao, Weiming
  • Huang, Weizhang
  • Russell, Robert D.

Abstract

Error indicators based on solution gradients, interpolation errors, and a posteriori error estimates are presented for use in defining monitor functions for the r-adaptive finite element methods based on moving mesh partial differential equations. The methods are compared with a careful selection of examples. The numerical results show that the methods based on both interpolation errors and a posteriori error estimates work well and have better performance than that based on the solution gradient. Since, the interpolation error is in general easier and more economic to compute than a posteriori error estimates, this study suggests that the error indicator based on interpolation errors be used for the r-adaptive method.

Suggested Citation

  • Cao, Weiming & Huang, Weizhang & Russell, Robert D., 2001. "Comparison of two-dimensional r-adaptive finite element methods using various error indicators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(2), pages 127-143.
    • Handle: RePEc:eee:matcom:v:56:y:2001:i:2:p:127-143
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