An optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems

In this paper, proper orthogonal decomposition (POD) is combined with the Petrov-Galerkin least squares mixed finite element (PLSMFE) method to derive an optimizing reduced PLSMFE formulation for the non-stationary conduction-convection problems. Error estimates between the optimizing reduced PLSMFE solutions based on POD and classical PLSMFE solutions are presented. The optimizing reduced PLSMFE formulation can circumvent the constraint of Babuska-Brezzi 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 PLSMFE solutions are consistent with theoretical results. Moreover, they have also shown the feasibility and efficiency of the POD method. Copyright (C) 2008 John Wiley & Sons, Ltd.