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A posteriori error estimates for mixed finite element discretizations of the Neutron Diffusion equations

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Abstract

We analyse $a\ posteriori$ error estimates for the discretization of the neutron diffusion equations with mixed finite elements. We provide guaranteed and locally efficient estimators on a base block equation, the one-group neutron diffusion equation. We pay particular attention to AMR strategies on Cartesian meshes, since such structures are common for nuclear reactor core applications. We exhibit a robust marker strategy for this specific constraint, the $direction\ marker$ strategy. The approach is further extended to a Domain Decomposition Method, the so-called DD+$L^2$ jumps method, as well as to the multigroup neutron diffusion equation.
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Dates and versions

cea-02893125 , version 1 (08-07-2020)

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Patrick Ciarlet, Minh Hieu Do, François Madiot. A posteriori error estimates for mixed finite element discretizations of the Neutron Diffusion equations. 2020. ⟨cea-02893125⟩

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