# Original geometrical stopping criteria associated to multilevel adaptive mesh refinement for problems with local singularities

* Corresponding author
1 LSC - Laboratoire de Simulation du Comportement des Combustibles
SESC - Service d'Etudes de Simulation du Comportement du combustibles : DEN/DEC/SESC
Abstract : This paper introduces a local multilevel mesh refinement strategy that automatically stops relating to a user-defined tolerance even incase of local singular solutions. Refinement levels are automatically generated thanks to a criterion based on the direct comparison of the a posteriori error estimate with the prescribed error. Singular solutions locally increase with the mesh step (e.g. load discontinuities, point load or geometric induced singularities) and are hence characterized by locally large element-wise error whatever the mesh refinement. Then, the refinement criterion may not be self-sufficient to stop the refinement process. Additional stop-ping criteria are required to avoid an infinite refinement process while still respecting the desired threshold. Two original geometry-based stopping criteria are proposed that consist in determining the critical region for which the mesh refinement becomes inefficient. Numerical examples show the efficiency of the methodology for stress tensor approximation in $L^2$-relative or $L^\infty$-absolute norms.
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https://hal-cea.archives-ouvertes.fr/cea-02339927
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### Citation

Isabelle Ramière, Hao Liu, Frédéric Lebon. Original geometrical stopping criteria associated to multilevel adaptive mesh refinement for problems with local singularities. Computational Mechanics, Springer Verlag, 2018, 64 (3), pp.645-661. ⟨10.1007/s00466-019-01674-7⟩. ⟨cea-02339927⟩

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