An optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems
Zhendong Luo, Jing Chen, I.M. Navon
In this work, proper orthogonal decomposition (POD) is combined with Petrov-Galerkin least squares mixed finite element (PLSMFE) method to derive an optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems. Error estimates between the optimizing reduced PLSMFE solutions based on POD and classical MFE solutions are presented. The optimizing reduced PLSMFE formulation can circumvent the constraint of Babuska-Brezzi (BB) condition so that the combination of finite element subspaces can be chosen freely and allow optimal order error estimates to be obtained. Numerical simulation examples have shown that the errors between the optimizing reduced PLSMFE solutions and the classical MFE solutions are consistent with theoretical results. Moreover, they have also shown the feasibility and efficiency of POD method.