Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical Pacific Ocean reduced gravity model

In this paper, the tropical Pacific Ocean reduced gravity model is studied using the proper orthogonal decomposition (POD) technique of mixed finite element (MFE) method and an error estimate of POD approximate solution based on MFE method is derived. POD is a model reduction technique for the simulation of physical processes governed by partial differential equations, e.g., fluid flows or other complex flow phenomena. It is shown by numerical examples that the error between POD approximate solution and reference solution is consistent with theoretical results, thus validating the feasibility and efficiency of POD method.