An optimal a priori error estimate for nonlinear multibody contact problems

S. Hüeber, B. I. Wohlmuth

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Abstract

Nonconforming domain decomposition methods provide a powerful tool for the numerical approximation of partial differential equations. For the discretization of a nonlinear multibody contact problem, we use linear mortar finite elements based on dual Lagrange multipliers. Under some regularity assumptions on the solution, an optimal convergence order of h0.5+v, 0 < v ≤ 0.5, can be established in two dimensions (2D) and three dimensions (3D). Compared with a standard linear saddle point formulation, two additional terms which provide a measure for the nonconformity and the nonlinearity of the approach have to be taken in account. Numerical examples illustrating the performance of the nonconforming method and confirming our theoretical result are presented.

Original languageEnglish
Pages (from-to)156-173
Number of pages18
JournalSIAM Journal on Numerical Analysis
Volume43
Issue number1
DOIs
StatePublished - 2005
Externally publishedYes

Keywords

  • A priori error estimates
  • Dual lagrange multipliers
  • Linear elasticity
  • Mortar finite element methods
  • Multibody contact problems

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