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

  • Isabelle RamièreEmail author
  • Hao Liu
  • Frédéric Lebon
Original Paper


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 \(L^\infty \)-absolute norms.


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



This work has been achieved in the framework of the collaboration protocol between the CEA (Commissariat à l’Énergie Atomique et aux Énergies Alternatives) and the LMA (Laboratoire de Mécanique et d’Acoustique, CNRS, Marseille). The authors are grateful to the PLEIADES project, financially supported by CEA, EDF (Électricité de France) and AREVA, that funded this research work.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.CEA, DEN, DEC, SESC, LSCSaint-Paul Lez DuranceFrance
  2. 2.CNRS, Centrale Marseille, LMAAix-Marseille UniversityMarseille cedex 13France

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