Publication: A posteriori estimation of dimension reduction errors
A posteriori estimation of dimension reduction errors
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Repin, S., Sauter, S., & Smolianski, A. (2004). A posteriori estimation of dimension reduction errors. In M. Feistauer (Ed.), Numerical mathematics and advanced applications (pp. 716–725). Springer. https://doi.org/10.1137/030602381
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A new a posteriori error estimator is presented for the verification of the dimensionally reduced models stemming from the elliptic problems on thin domains. The original problem is considered in a general setting, without any specific assumptions on the domain geometry, coefficients and the right-hand sides. The estimator provides a guaranteed upper bound for the modelling error in the energy norm, exhibits the optimal convergence rate as the domain thickness tends to zero and accurately indicates the local error distribution.
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- Repin, S
- Sauter, S
- Smolianski, A
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Repin, S., Sauter, S., & Smolianski, A. (2004). A posteriori estimation of dimension reduction errors. In M. Feistauer (Ed.), Numerical mathematics and advanced applications (pp. 716–725). Springer. https://doi.org/10.1137/030602381
