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September 17, 2026ESAIM Mathematical Modelling and Numerical Analysis

The finite element method for the elastic body with the Tresca friction and a modified Signorini-type contact interface conditions

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Authors

ZLZhen LiTKTakahito KashiwabaraGZGuanyu Zhou

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Overview

Computational analysis demonstrates stable finite element approximations for dynamic elastic bodies with frictional contact interfaces, highlighting efficient iterative solvers for contact mechanics.

Key Points

  • Formulate and analyze semi-discrete and fully discrete finite element schemes for dynamic linear elastic bodies undergoing Tresca friction and generalized Signorini-type contact.
  • Formulated semi-discrete and fully discrete approximations using a mass-lumping technique for contact terms, expressed as variational inequalities and Lagrange multiplier systems.
  • Proved mathematical well-posedness, numerical stability, and error bounds using regularization techniques under specific time-step restrictions.
  • Implemented and evaluated Uzawa, active/inactive set, and augmented Lagrangian iterative algorithms to solve the resulting discrete contact systems.
  • Established theoretical well-posedness, stability, and error estimates for the semi-discrete finite element scheme.
  • Demonstrated guaranteed convergence and stability of the fully discrete scheme subject to a defined time-step restriction.
  • Confirmed theoretical convergence rates and established computational efficiency across all proposed iterative solvers using numerical experiments.

Cite This Study

Li et al. (2026) studied this question.

synapsesocial.com/papers/6aabb6635f706d05830e4c7ehttps://doi.org/10.1051/m2an/2026077
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