Numerical study of natural superconvergence in least-squares finite element methods for elliptic problems |
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| Authors: | Runchang Lin Zhimin Zhang |
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| Institution: | (1) Department of Mathematical and Physical Sciences, Texas A&M International University, Laredo, Texas 78041-1900, USA;(2) Department of Mathematics, Wayne State University, Detroit, Michigan 48202-3622, USA |
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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.
The second author was supported in part by the US National Science Foundation under Grant DMS-0612908. |
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| Keywords: | least-squares mixed finite element method natural superconvergence Raviart-Thomas element |
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