On convergence of the penalty method for unilateral contact problems

Franz Chouly (1) , Patrick Hild (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We present a convergence analysis of the penalty method applied to unilateral contact problems in two and three space dimensions. We first consider, under various regularity assumptions on the exact solution to the unilateral contact problem, the convergence of the continuous penalty solution as the penalty parameter $\varepsilon$ vanishes. Then, the analysis of the finite element discretized penalty method is carried out. Denoting by $h$ the discretization parameter, we show that the error terms we consider give the same estimates as in the case of the constrained problem when the penalty parameter is such that $\varepsilon = h$.

Mots clés: unilateral contact; variational inequality; finite elements; penalty method; a priori error estimates

Domaines: Analyse numérique [math.NA]

Franz Chouly, Patrick Hild. On convergence of the penalty method for unilateral contact problems. Applied Numerical Mathematics, 2013, 65, pp.27-40. ⟨10.1016/j.apnum.2012.10.003⟩. ⟨hal-00688641⟩