A Posteriori Error Estimation for the Dirichlet Problem with Account of the Error in the Approximation of Boundary Conditions

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1, independently of the discretization method chosen. In particular, our error estimator can be applied also to problems and discretizations where the Galerkin orthogonality is not available. We will present different strategies for the evaluation of the error estimator. Only one constant appears in its definition which is the one from Friedrichs' inequality; that constant depends solely on the domain geometry, and the estimator is quite non-sensitive to the error in the constant evaluation. Finally, we show how accurately the estimator captures the local error distribution, thus, creating a base for a justified adaptivity of an approximation.

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Received April 15, 2002; revised March 10, 2003 Published online: June 23, 2003

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Repin, S., Sauter, S. & Smolianski, A. A Posteriori Error Estimation for the Dirichlet Problem with Account of the Error in the Approximation of Boundary Conditions. Computing 70, 205–233 (2003). https://doi.org/10.1007/s00607-003-0013-7

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  • 2000 Mathematics Subject Classification: 35J20, 65N15, 65N30.
  • Keywords and phrases: A posteriori error estimate, duality technique, reliability, efficiency, local error distribution.