Abstract
In this paper, two characteristic methods are introduced to solve the thermal convection problems with infinite Prandtl number on nonuniform staggered grids. We obtain spatial second order superconvergence in the discrete L2 norm for the temperature, velocity and pressure. Besides, second order superconvergence in the discrete H1 norm for both the temperature and some terms of the velocity on nonuniform grids is established. First and second order time discretizations of the thermal balance equation are provided. Numerical experiments are presented to show that the convergence rates are in agreement with the theoretical analysis.
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