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A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

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Abstract

A residual type a posteriori error estimator is presented and analyzed for Weak Galerkin finite element methods for second order elliptic problems. The error estimator is proved to be efficient and reliable through two estimates, one from below and the other from above, in terms of an \(H^1\)-equivalent norm for the exact error. Two numerical experiments are conducted to demonstrate the effectiveness of adaptive mesh refinement guided by this estimator.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Irvine, Irvine, CA, 92697, USA

    Long Chen

  2. Division of Mathematical Sciences, National Science Foundation, Arlington, VA, 22230, USA

    Junping Wang

  3. Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Xiu Ye

Authors
  1. Long Chen
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  2. Junping Wang
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  3. Xiu Ye
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Corresponding author

Correspondence to Long Chen.

Additional information

Long Chen: This research was supported in part by National Science Foundation Grant DMS-1115961 and in part by Department of Energy prime award # DE-SC0006903.

Junping Wang: The research of Wang was supported by the NSF IR/D program, while working at National Science Foundation. However, any opinion, finding, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

Xiu Ye: This research was supported in part by National Science Foundation Grant DMS-1115097.

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Chen, L., Wang, J. & Ye, X. A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems. J Sci Comput 59, 496–511 (2014). https://doi.org/10.1007/s10915-013-9771-3

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  • DOI: https://doi.org/10.1007/s10915-013-9771-3

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