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A finite volume element formulation and error analysis for the non-stationary conduction-convection problem. (English) Zbl 1248.35163
Summary: The non-stationary conduction-convection problem including the velocity vector field and the pressure field as well as the temperature field is studied with a finite volume element (FVE) method. A fully discrete FVE formulation and the error estimates between the fully discrete FVE solutions and the accuracy solution are provided. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary conduction-convection problem and is one of the most effective numerical methods by comparing the results of the numerical simulations of the FVE formulation with those of the numerical simulations of the finite element method and the finite difference scheme for the non-stationary conduction-convection problem.

MSC:
35Q35 PDEs in connection with fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
65Z05 Applications to the sciences
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