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A weak finite element method for elliptic problems in one space dimension

Author

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  • Zhang, Tie
  • Tang, Lixin

Abstract

We present a weak finite element method for elliptic problems in one space dimension. Our analysis shows that this method has more advantages than the known weak Galerkin method proposed for multi-dimensional problems, for example, it has higher accuracy and the derived discrete equations can be solved locally, element by element. We derive the optimal error estimates in the discrete H1-norm, the L2-norm and L∞-norm, respectively. Moreover, some superconvergence results are also given. Finally, numerical examples are provided to illustrate our theoretical analysis.

Suggested Citation

  • Zhang, Tie & Tang, Lixin, 2016. "A weak finite element method for elliptic problems in one space dimension," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 1-10.
    • Handle: RePEc:eee:apmaco:v:280:y:2016:i:c:p:1-10
    DOI: 10.1016/j.amc.2016.01.018
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