Abstract
In this paper, a method which reconstructs an H(div)-conforming local equilibrated flux is presented for equilibrated flux-based a posteriori error estimate for the finite element method of the second-order elliptic problem. The flux is reconstructed in the lowest-order Raviart–Thomas spaces for finite element approximation. For a simplicial mesh, the reconstruction which performed on every element rather than on the patch of the elements of the mesh or on the dual mesh is achieved by solving a third (or fourth)-order linear equations on every element and a second-order linear equations on every edge or face. So, the amount of computational work is small. Numerical examples demonstratex the effectiveness and improvements of our method.
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More From: International Journal of Modeling, Simulation, and Scientific Computing
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