Rigorous and effective a-posteriori error bounds for nonlinear problems—application to RB methods
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DOI: 10.1007/s10444-020-09741-x
Abstract: Quantifying the error that is induced by numerical approximation techniques is an important task in many fields of applied mathematics. Two characteristic properties of error bounds that are desirable are reliability and efficiency. In this… read more here.
Keywords: mathematics; error; error bounds; rigorous effective ... See more keywords
The calculation of the reliability index in nonlinear problems: A new method
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DOI: 10.1016/j.asej.2019.11.008
Abstract: Abstract The accurate estimation of the health (reliability) index is important to estimate probability of failure in the reliability assessment of structures. The conventional first-order reliability methods including the Hasofer-Lind, Rackwitz-Fiessler, and Monte Carlo could… read more here.
Keywords: reliability; proposed method; reliability index; nonlinear problems ... See more keywords
A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics
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DOI: 10.1016/j.cma.2017.06.011
Abstract: Abstract When relying on Newton iterations to solve nonlinear problems in the context of Reduced Basis (RB) methods, the assembling of the RB arrays during the online stage depends on the dimension of the underlying… read more here.
Keywords: model; deim technique; nonlinear problems; deim ... See more keywords
Nonlinear problems on the Sierpiński gasket
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.03.032
Abstract: Abstract This paper concerns with a class of elliptic equations on fractal domains depending on a real parameter. Our approach is based on variational methods. More precisely, the existence of at least two non-trivial weak… read more here.
Keywords: sierpi ski; nonlinear problems; ski gasket; problems sierpi ... See more keywords