Gradient recovery type a posteriori error estimate for finite element approximation on non-uniform meshes

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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