A defect-correction method for unsteady conduction-convection problems II: Time discretization

Authors:
Zhiyong Si;Yinnian He;Tong Zhang
Affiliations:
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, PR China;Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China;School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

In this paper, a fully discrete defect-correction mixed finite element method (MFEM) for solving the non-stationary conduction-convection problems in two dimension, which is leaded by combining the Back Euler time discretization with the two-step defect correction in space, is presented. In this method, we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct these solutions on the same grid using a linearized defect-correction technique. The stability and the error analysis are derived. The theory analysis shows that our method is stable and has a good convergence property. Some numerical results are also given, which show that this method is highly efficient for the unsteady conduction-convection problems.