Summary
This study establishes an error estimate for a penalty-finite element approximation of the variational inequality obtained by a class of obstacle problems. By special identification of the penalty term, we first show that the penalty solution converges to the solution of a mixed formulation of the variational inequality. The rate of convergence of the penalization is ɛ where ɛ is the penalty parameter. To obtain the error of finite element approximation, we apply the results obtained by Brezzi, Hager and Raviart for the mixed finite element method to the variational inequality.
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Kikuchi, N. Convergence of a penalty-finite element approximation for an obstacle problem. Numer. Math. 37, 105–120 (1981). https://doi.org/10.1007/BF01396189
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DOI: https://doi.org/10.1007/BF01396189