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Some stability results for frictionless contact problems in elastodynamics formulated with Nitsche’s method
Franz Chouly1; Hao Huang2; Nicolas Pignet3
1Centro de Matemática (CMAT), IRL-2030 CNRS IFUMI, Facultad de Ciencias, Universidad de la República, 11400 Montevideo, Uruguay.
2EDF Lab Paris-Saclay, 7 boulevard Gaspard Monge, 91120 Palaiseau, France — Institut de Mathématiques de Bourgogne, Université de Bourgogne, 21078 Dijon, France.
3EDF Lab Paris-Saclay, 7 boulevard Gaspard Monge, 91120 Palaiseau, France.
The SMAI Journal of computational mathematics, Volume 12 (2026), pp. 289-329

This work focuses on the numerical performance of the Nitsche-based Finite Element Method for dynamic unilateral contact problems combined with two implicit one-step time-marching schemes. The non-linear contact boundary conditions cause irregularities, which may lead to unstable performance and potential divergence during simulations. By focusing on the discontinuities inherent in dynamic contact problems, we provide new stability results for the proposed methods.

Published online:
DOI: 10.5802/smai-jcm.150
Classification: 65M22, 65N30, 65L60
Keywords: Time-marching schemes, Nitsche’s method, unilateral contact, finite element method, elastodynamics

Franz Chouly  1 ; Hao Huang  2 ; Nicolas Pignet  3

1 Centro de Matemática (CMAT), IRL-2030 CNRS IFUMI, Facultad de Ciencias, Universidad de la República, 11400 Montevideo, Uruguay.
2 EDF Lab Paris-Saclay, 7 boulevard Gaspard Monge, 91120 Palaiseau, France — Institut de Mathématiques de Bourgogne, Université de Bourgogne, 21078 Dijon, France.
3 EDF Lab Paris-Saclay, 7 boulevard Gaspard Monge, 91120 Palaiseau, France. 
Franz Chouly; Hao Huang; Nicolas Pignet. Some stability results for frictionless contact problems in elastodynamics formulated with Nitsche’s method. The SMAI Journal of computational mathematics, Volume 12 (2026), pp. 289-329. doi: 10.5802/smai-jcm.150
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