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Finite element formulation based on proper orthogonal decomposition for parabolic equations. (English) Zbl 1183.65122
The authors are concerned with the study of the proper orthogonal decomposition (POD) method used to a usual finite element (FE) formulation for parabolic equations so that the usual finite element formulation is reduced into a (POD)-(FE) formulation with lower dimensional numbers and enough high accuracy. The errors between the reduced (POD)-(FE) solution and the usual (FE) solution are analyzed. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions.
MSC:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
35K61Nonlinear parabolic equations, nonlinear initial boundary value problems
65M15Error bounds (IVP of PDE)
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