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

Tie Zhang and Lixin Tang

Applied Mathematics and Computation, 2016, vol. 280, issue C, 1-10

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.

Keywords: Weak finite element method; Stability; Optimal error estimate; Superconvergence; Elliptic problem in one space dimension (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:280:y:2016:i:c:p:1-10

DOI: 10.1016/j.amc.2016.01.018

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