A reduced finite element formulation based on proper orthogonal decomposition for Burgers equation

A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for Burgers equation such that it is reduced into a POD FE formulation with lower dimensions 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. Moreover, this validates the feasibility and efficiency of the POD method.