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A reduced finite element formulation based on proper orthogonal decomposition for Burgers equation. (English) Zbl 1169.65096
The authors apply a proper orthogonal decomposition (POD) method to a usual finite element (FE) formulation for sufficiently Burgers equation such that it is reduced into a POD FE formulation with lower dimensions and 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. This validates the feasibility and efficiency of the POD method.
MSC:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
65M15Error bounds (IVP of PDE)
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