一类非线性对流占优扩散方程的预测-校正差分流线扩散(PC-FDSD)方法

THE PREDICTOR-CORRECTOR FDSD METHOD FOR A KIND OF TIME DEPENDENT NONLINEAR CONVECTION-DIFFUSION PROBLEMS

本文对一类发展型对流占优扩散方程 ,建立了预测 -校正差分流线扩散 ( PG-FDSD)方法 ,给出了该方法的误差估计 ,理论分析表明 ,当时间步长 Δt和空间网格参数 h相匹配时 ,该格式的误差在 h方向按 L∞ ( L2( Ω) )模是拟丰满的 ,在时间方向上的精度则为 3 / 2阶 .数值算例的结果表明 ,PC-FDSD方法是求解此类问题的一种有效的方法 .

In this paper, a PC FDSD scheme is presented and analyzed for a kind of time dependent nonlinear convection diffusion problems. The scheme is constructed and it's error estimation is established.. Through the theoretical analysis, if the time step Δt and the mesh parameter h are matched, the convergence order of this scheme can be proved as quasi optimal in L 2(Ω) norm in h and 3/2 order in Δt . The numerical example also shows that this scheme is efficient to solve this kind of problem.