Comparison principles applied to obstacle problems with penalties

Adam, Stefan; Großmann, Christian

doi:10.1080/01630569508816663

Cited by 2 publications

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“…. , N. For a detailed study of further properties of problems of this type and, in particular, the behavior of Newton's method applied to (6.9) using a fixed parameter s > 0 we refer to [1,6]. In the present paper we concentrate our attention to iterations where only one Newton step at each parameter s = s k level is performed.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Referring e.g. to [1,6,8,14,24,25] the reader should be aware that, as a rule, tedious analysis is necessary to obtain such estimates in an appropriate norm for each case of a particular singular embedding technique. Moreover, studies of the convergence of Newton's method applied to such highly nonlinear problems require specific tools as developed e.g.…”

Section: Introductionmentioning

confidence: 99%

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Parameter selection rules for path-following with singular embedding

Großmann

Ismail

1999

Numerische Mathematik

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Singular embedding methods require appropriately adjusted parameters to guarantee the contraction of locally quadratically convergent iterative methods. Firstly some general rule for the parameter selection is proposed and its rate of convergence is analyzed. Secondly, some modifications in the case of polynomial error and contraction bounds are studied. Finally, these results are applied to the embedding of an elliptic boundary value problem with discontinuous nonlinearities into a family of smooth problems. Here the regularization is done in such a way that the solutions of the resulting auxiliary problems require only one step of Newton's method. Classification (1991): 35J60, 35R05, 49L10, 65K10, 65H20 Mathematics Subject

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Section: Numerical Experimentsmentioning

confidence: 99%