Summary
In this paper the Wilson nonconforming finite element is considered for solving a class of two-dimensional second-order elliptic boundary value problems. Superconvergence estimates and error expansions are obtained for both uniform and non-uniform rectangular meshes. A new lower bound of the error shows that the usual error estimates are optimal. Finally a discussion on the error behaviour in negative norms shows that there is generally no improvement in the order by going to weaker norms.
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This work was supported by the National Natural Science Foundation of P. R. China and Deutsche Forschungsgemeinschaft, SFB 359, Germany
This work is part of the Transitions and Defects in Ordered Materials Project and was supported in part by the NSF through grant DMS 911-1572, by the AFOSR through grant AFOSR-91-0301, by the ARO through grants DAAL03-89-G-0081 and DAAL03-92-G-0003, and by a grant from the Minnesota Supercomputer Institute
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Chen, H., Li, B. Superconvergence analysis and error expansion for the Wilson nonconforming finite element. Numer. Math. 69, 125–140 (1994). https://doi.org/10.1007/s002110050084
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DOI: https://doi.org/10.1007/s002110050084