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Variational h-adaption for coupled thermomechanical problems

Rohit Pethe (Research Institute in Civil and Mechanical Engineering, Ecole Centrale de Nantes, Nantes, France)
Thomas Heuzé (Research Institute in Civil and Mechanical Engineering, Ecole Centrale de Nantes, Nantes, France)
Laurent Stainier (Research Institute in Civil and Mechanical Engineering, Ecole Centrale de Nantes, Nantes, France)

Engineering Computations

ISSN: 0264-4401

Article publication date: 25 November 2019

Issue publication date: 16 April 2020



The purpose of this paper is to present a variational mesh h-adaption approach for strongly coupled thermomechanical problems.


The mesh is adapted by local subdivision controlled by an energy criterion. Thermal and thermomechanical problems are of interest here. In particular, steady and transient purely thermal problems, transient strongly coupled thermoelasticity and thermoplasticity problems are investigated.


Different test cases are performed to test the robustness of the algorithm for the problems listed above. It is found that a better cost-effectiveness can be obtained with that approach compared to a uniform refining procedure. Because the algorithm is based on a set of tolerance parameters, parametric analyses and a study of their respective influence on the mesh adaption are carried out. This detailed analysis is performed on unidimensional problems, and a final example is provided in two dimensions.


This work presents an original approach for independent h-adaption of a mechanical and a thermal mesh in strongly coupled problems, based on an incremental variational formulation. The approach does not rely on (or attempt to provide) error estimation in the classical sense. It could merely be considered to provide an error indicator. Instead, it provides a practical methodology to adapt the mesh on the basis of the variational structure of the underlying mathematical problem.



Authors’ contributions: LS proposed the initial idea sustaining this work. RP implemented the methods and performed all test cases, under supervision of TH and LS. RP drafted the manuscript, and all co-authors contributed to revisions leading to the final manuscript.

Competing interests: The authors declare that they have no competing interests.

Funding: RP was funded by Centrale Nantes through Doctoral School SPIGA (ED 498).


Pethe, R., Heuzé, T. and Stainier, L. (2020), "Variational h-adaption for coupled thermomechanical problems", Engineering Computations, Vol. 37 No. 4, pp. 1261-1290.



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