Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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ROBUST A POSTERIORI ERROR ESTIMATOR FOR LOWEST-ORDER FINITE ELEMENT METHODS OF INTERFACE PROBLEMS

  • Received : 2016.03.24
  • Accepted : 2016.06.15
  • Published : 2016.06.25
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Abstract

In this paper we analyze an a posteriori error estimator based on flux recovery for lowest-order finite element discretizations of elliptic interface problems. The flux recovery considered here is based on averaging the discrete normal fluxes and/or tangential derivatives at midpoints of edges with weight factors adapted to discontinuous coefficients. It is shown that the error estimator based on this flux recovery is equivalent to the error estimator of Bernardi and $Verf{\ddot{u}}rth$ based on the standard edge residuals uniformly with respect to jumps of the coefficient between subdomains. Moreover, as a byproduct, we obtain slightly modified weight factors in the edge residual estimator which are expected to produce more accurate results.

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References

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