Search results for "Contraction mapping"

showing 3 items of 13 documents

Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem

2021

The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing the fixed-stress split scheme, which leads to an iteratively solved semi-discrete system. The error bounds are derived by combining a posteriori estimates for contractive mappings with functional type error control for elliptic partial differential equations. The estimates are applicable to any approximation in the admissible functional space and are independent of the discretization method. They are fully computable, do not contain mesh-dependent constants, and provide r…

DiscretizationPoromechanics010103 numerical & computational mathematicsContraction mappings01 natural sciencesFOS: MathematicsDecoupling (probability)Applied mathematicsMathematics - Numerical Analysis0101 mathematicsvirheanalyysiMathematicsa posteriori error estimatesosittaisdifferentiaaliyhtälötA posteriori error estimatesfixed-stress split iterative schemeBiot numberNumerical Analysis (math.NA)Biot problem010101 applied mathematicsComputational MathematicsBiot problem; Fixed-stress split iterative scheme; A posteriori error estimates; Contraction mappingsComputational Theory and MathematicsElliptic partial differential equationModeling and SimulationNorm (mathematics)contraction mappingsA priori and a posterioriFixed-stress split iterative schemenumeerinen analyysiapproksimointiError detection and correction
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Generalized countable iterated function systems

2011

One of the most common and most general way to generate fractals is by using iterated function systems which consists of a finite or infinitely many maps. Generalized countable iterated function systems (GCIFS) are a generalization of countable iterated function systems by considering contractions from X ? X into X instead of contractions on the metric space X to itself, where (X, d) is a compact metric space. If all contractions of a GCIFS are Lipschitz with respect to a parameter and the supremum of the Lipschitz constants is finite, then the associated attractor depends continuously on the respective parameter.

Hutchinson operatorDiscrete mathematicsMetric spaceIterated function systemCollage theoremGeneral MathematicsCountable setContraction mappingLipschitz continuityCosmic spaceMathematicsFilomat
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Graphical metric space: a generalized setting in fixed point theory

2016

Building on recent ideas of Jachymski, we work on the notion of graphical metric space and prove an analogous result for the contraction mapping principle. In particular, the triangular inequality is replaced by a weaker one, which is satisfied by only those points which are situated on some path included in the graphical structure associated with the space. Some consequences, examples and an application to integral equations are presented to confirm the significance and unifying power of obtained generalizations.

Pseudometric space01 natural sciencesGraphIntrinsic metricOrdered metric spaceSettore MAT/05 - Analisi MatematicaGraphical metric spaceContraction mapping0101 mathematicsMathematicsDiscrete mathematicsAlgebra and Number TheoryApplied MathematicsInjective metric space010102 general mathematicsFixed pointConvex metric space010101 applied mathematicsAlgebraComputational MathematicsMetric spaceGeometry and TopologySettore MAT/03 - GeometriaMetric differentialAnalysisFisher information metric
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