Proper Orthogonal Decomposition Approach and Error estimation of Mixed finite Element Methods for the tropical Pacific Ocean Reduced Gravity Model
Zhendong Luo, Jiang Zhu, Ruiwen Wang, I. Michael Navon
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, which 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, and an error estimate of POD approximate solution based on MFE method is derived. 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.