Analysis of a multilevel iterative method for nonlinear finite element equations

Authors:
Randolph E. Bank and Donald J. Rose

Journal:
Math. Comp. **39** (1982), 453-465

MSC:
Primary 65N30; Secondary 65H10

DOI:
https://doi.org/10.1090/S0025-5718-1982-0669639-X

MathSciNet review:
669639

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Abstract: The multilevel iterative technique is a powerful technique for solving the systems of equations associated with discretized partial differential equations. We describe how this technique can be combined with a globally convergent approximate Newton method to solve nonlinear partial differential equations. We show that asymptotically only one Newton iteration per level is required; thus the complexity for linear and nonlinear problems is essentially equal.

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DOI:
https://doi.org/10.1090/S0025-5718-1982-0669639-X

Article copyright:
© Copyright 1982
American Mathematical Society