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Error Estimates for the Boundary Element Approximation of a Contact Problem in Elasticity
Author(s) -
Spann W.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199702)20:3<205::aid-mma853>3.0.co;2-s
Subject(s) - mathematics , mathematical analysis , sobolev space , discretization , variational inequality , isotropy , boundary value problem , elasticity (physics) , uniqueness , boundary (topology) , linear elasticity , finite element method , physics , materials science , quantum mechanics , composite material , thermodynamics
The two‐dimensional frictionless contact problem of linear isotropic elasticity in the half‐space is treated as a boundary variational inequality involving the Poincare–Steklov operator and discretized by linear boundary elements. Quadratic growth of the energy near the solution is shown under weak regularity assumptions if the central axis of external forces intersects the boundary of the domain in a Lebesgue null set. Estimating the numerical range of the discrete Poincare–Steklov operator and properly modifying it, enables the application of an error estimate for semi‐coercive variational inequalities. Optimal order of convergence is obtained in the underlying Sobolev space H 1/2 (∂Ω) 2 . © 1997 by B.G. Teubner Stuttgart‐John Wiley & Sons, Ltd.