A modified Kacanov iteration scheme with application to quasilinear diffusion models
Keyword(s):
The classical Kacanov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation, we introduce a modified Kacanov method, which allows for (adaptive) damping, and, thereby, to derive a new convergence analysis under more general assumptions and for a wider range of applications. For instance, in the specific context of quasilinear diffusion models, our new approach does no longer require a standard monotonicity condition on the nonlinear diffusion coefficient to hold. Moreover, we propose two different adaptive strategies for the practical selection of the damping parameters involved.
2019 ◽
Vol 24
(1)
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pp. 147-169
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2019 ◽
Keyword(s):
2012 ◽
Vol 2
(2)
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pp. 105-112