5. Incremental form for corrector-step

The equations are written for the variable Y⁺ = X⁺_F - X^*_F (note again that the computation of Y⁺ from X⁺, X^* does not require any interpolation). Hence (4) writes:

$\begin{displaymath}\frac{Y^+ + X^*_F - X^0_{O^*}}{\Delta t} = \frac{(1+ \epsilon... ...frac{(1+ \epsilon) X^*_F + (1 - \epsilon) X^0_{O^*}}{2}\right) \end{displaymath}$

$\Longrightarrow$

$\begin{displaymath}\frac{Y^+ + X^*_F - X^0_{O^*}}{\Delta t} = \frac{(1+ \epsilon... ...}) }{2} + {\bf L}^*\left(\frac{(1+ \epsilon) Y^+ }{2} \right) \end{displaymath}$

$\Longrightarrow$

$\begin{displaymath}\left[{\bf I} - (1 + \epsilon) \frac{\Delta t}{2} {\bf L}^*\r... ...ilon) {\bf M}(X^*_F) + (1- \epsilon){\bf M}(X^0_{O^*}) \right] \end{displaymath}$

(6)

In this case also there is no linear contribution in the RHS for the corrector-step as it was for the predictor-step.

Pierre BENARD
2002-06-17

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