A posteriori estimation of dimension reduction errors. (English) Zbl 1056.65105

Feistauer, M. (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18–22, 2003. Berlin: Springer (ISBN 3-540-21460-7/hbk). 716-725 (2004).
Summary: 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.
For the entire collection see [Zbl 1046.65002].


65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74K20 Plates
74S05 Finite element methods applied to problems in solid mechanics