Researches Of Methods Of Numerical Solution Based On Proper Orthogonal Decomposition Technology For Burgers Equations

A proper orthogonal decomposition (POD) method is applied to a usual finite difference (FD) formulation and a usual finite element (FE) formulation for Burgers equations so that they can be reduced into a POD FD formulation and a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FD and FE solutions and the usual FD and FE solutions are analyzed. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.