Abstract
In this paper, we derive gradient recovery type a posteriori error estimate for the finite element approximation of elliptic equations. We show that a posteriori error estimate provide both upper and lower bounds for the discretization error on the non-uniform meshes. Moreover, it is proved that a posteriori error estimate is also asymptotically exact on the uniform meshes if the solution is smooth enough. The numerical results demonstrating the theoretical results are also presented in this paper.
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Du, L., Yan, N. Gradient recovery type a posteriori error estimate for finite element approximation on non-uniform meshes. Advances in Computational Mathematics 14, 175–193 (2001). https://doi.org/10.1023/A:1016676917360
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DOI: https://doi.org/10.1023/A:1016676917360