Computational Science Asked on October 23, 2021
https://www.jstor.org/stable/pdf/2157482.pdf, here I have a problem in last equation of (2.6) in section (2.1). When they are considering error equation on the interface $Gamma$ they get $e_v^{(n)} = delta_n$, where $delta_n = lambda_n – lambda_{n-1}$(Here I use there definition of $delta_2 = lambda_2-lambda_1$, given below equation (2.7)).
If I calculate $e_v^{(n)}$ on $Gamma,$ I find something like this, $e_v^{(n)} = v^{(n)} – v|_{Gamma} = lambda_n – v|_{Gamma}$ = $lambda_n -lambda_{n-1} + lambda_{n-1} – v|_{Gamma}$ = $delta_n – e_{v}^{(n-1)}.$
Thanking you.
$delta_n neq lambda_n - lambda_{n-1}$. It is actually defined in (2.8) and (I don't know why) $delta_2 = lambda_2 - lambda_1$. You can confirm it by subtracting first three lines of (2.2) from (2.3) which will give you (2.6).
Section 2.1 is the convergence analysis of the algorithm, so it is okay if $delta_1$ is not explicitly defined. Actual algorithm is given in (2.3)-(2.5), in which case, you would choose $lambda_1$ as a proper initial guess. Probably zero would be an okay one.
Answered by Abdullah Ali Sivas on October 23, 2021
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