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Numerical study of natural superconvergence in least-squares finite element methods for elliptic problems

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Abstract

Natural superconvergence of the least-squares finite element method is surveyed for the one-and two-dimensional Poisson equation. For two-dimensional problems, both the families of Lagrange elements and Raviart-Thomas elements have been considered on uniform triangular and rectangular meshes. Numerical experiments reveal that many superconvergence properties of the standard Galerkin method are preserved by the least-squares finite element method.

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Correspondence to Runchang Lin.

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Dedicated to Ivan Hlaváček on the occasion of his 75th birthday

The second author was supported in part by the US National Science Foundation under Grant DMS-0612908.

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Lin, R., Zhang, Z. Numerical study of natural superconvergence in least-squares finite element methods for elliptic problems. Appl Math 54, 251–266 (2009). https://doi.org/10.1007/s10492-009-0016-6

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