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A posteriori existence in numerical computations
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Ortner, Christoph (2009) A posteriori existence in numerical computations. SIAM Journal on Numerical Analysis, Vol.47 (No.4). pp. 2550-2577. doi:10.1137/060668183 ISSN 0036-1429.
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Official URL: http://dx.doi.org/10.1137/060668183
Abstract
A typical a posteriori error analysis for numerical methods for differential equations consists of two elements: the stability of the continuous problem and an a posteriori computed residual estimate. If the problem is nonlinear, then this is possible only if it is strongly monotone. In this paper, we will estimate the stability constant a posteriori as well, in order to apply the inverse function theorem to derive the existence of solutions from the numerical computation, and thus obtain rigorous a posteriori error estimates for nonmonotone equations.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | SIAM Journal on Numerical Analysis | ||||
Publisher: | Society for Industrial and Applied Mathematics | ||||
ISSN: | 0036-1429 | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.47 | ||||
Number: | No.4 | ||||
Page Range: | pp. 2550-2577 | ||||
DOI: | 10.1137/060668183 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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