對於拋物型方程的數值解, 我們通常利用時間變數的隱方法如:Crank-Nicolson法, 而在使用古典交替方向法對空間變數離散時, 有時伴隨著交替方向法的分裂誤差會比原來的Crank-Nicolson法的誤差還要大, 我們希望藉由一個修正項的增加使的這個分裂誤差縮小, 並且這個新增的修正項並不需要增加太多的計算量, 我們計畫使用有限混合元法來在其空間變數上作離散, 我們需要導推這個方法收斂性。

Classical alternating direction (AD) methods for parabolic equations, based on some standard implicit time stepping procedure such as Crank-Nicolson, can have errors associated with the AD perturbations that are much larger than the errors associated with the underlying time stepping procedure . We plan to show that minor modifications in the AD procedures can virtually eliminate the perturbation errors at an minor additional computational cost. A mixed finite element method is applied in the spactial variables. Similar to the finite difference and finite element methods in spactial variables, we plan to have the same accuracy in time. A convergence analysis can also be shown .

1.Introduction 4
2.The Mixed Finite Method 6
3.AD algorithms 11
4.AD-M algorithms 13
5.Modified AD algorithms for mixed finite element 14
6.Numerical result 22
7.Conclusions 31

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