Topics in Numerical Partial Differential Equations and Scientific Computing by Susanne C. Brenner

Author:Susanne C. Brenner
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

4.1 Least Squares Method

In this section, we are going to redefine the minimization problem as a least squares problem.

Set and define the operator as

(4.5)

where is the solution of (4.2) and is the solution of (4.3).

The minimization of the functional in (4.4) is then equivalent to the minimization of the least squares function , that is:

(4.6)

We solve this problem by a residual updating technique. First, an initial guess for a minimizer, , is chosen and is computed. Since we expect that for a sufficiently small at the minimizer, we take as a residual and find a correction for such that

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