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

Isabelle Ramière (1) , Hao Liu (2) , Frédéric Lebon (3)

1 LSC - Laboratoire de Simulation du Comportement des Combustibles
2 Shanghai Jiao Tong University [Shanghai]
3 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

This paper introduces a local multilevel mesh refinement strategy that automatically stops relating to a user-defined tolerance even in case 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 local 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 stopping criteria are required if no physical-designed estimator wants to be used. Two original geometry-based stopping criteria are proposed that consist in automatically 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 ∞-absolute norms.

Mots clés: A posteriori error estimator; Elastostatics; Adaptive mesh refinement; Local Defect Correction method; Stopping criteria Local singular solution

Domaines: Mécanique des solides [physics.class-ph]

Isabelle Ramière, Hao Liu, Frédéric Lebon. Original geometrical stopping criteria associated to multilevel adaptive mesh refinement for problems with local singularities. Computational Mechanics, 2019, 64 (3), pp.645-661. ⟨10.1007/s00466-019-01674-7⟩. ⟨hal-02336644⟩