A defect-correction method for unsteady conduction-convection problems. I: Spatial discretization
The authors investigate spatial problems for non-stationary conduction-convection equations. The coupled equations govern viscous incompressible flow and heat transfer, using the Boussinesq approximations to non-stationary Navier-Stokes equations. A new semi-discrete defect-correction finite element method for non-stationary conduction-convection problems is investigated from the numerical point of view. The main idea for the proposed method is to involve an artificial viscosity term as a stabilizing factor for both velocity and temperature equations. Then the nonlinear problem is solved only once on a finite grid, and the corrections are achieved in an iterative way by solving linear problems on the same finite grid. Using the previous results of \textit{Z. Luo} [Chin. J. Numer. Math. Appl. 20, No.~2, 29--59 (1998; Zbl 0919.76050)] where under some assumptions on the continuous solution the unique solution and stability results for the continuous as well as for the classical finite element discrete problem were proved, the authors prove the stability of their scheme for both the nonlinear discrete problem and the linear one. Finally, an error analysis for both problems is given in appropriate functional spaces.
scientific article; zbMATH DE number 5916762
scientific article