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A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework. (English) Zbl 1398.74375

Summary: Today industries do not only require fast simulation techniques but also verification techniques for the simulations. The proper generalized decomposition (PGD) has been situated as a suitable tool for fast simulation for many physical phenomena. However, so far, verification tools for the PGD are under development. The PGD approximation error mainly comes from two different sources. The first one is related with the truncation of the PGD approximation and the second one is related with the discretization error of the underlying numerical technique. In this work, we propose a fast error indicator technique based on recovery techniques, for the discretization error of the numerical technique used by the PGD technique, for refinement purposes.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74B05 Classical linear elasticity
76M10 Finite element methods applied to problems in fluid mechanics
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