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Gotowa bibliografia na temat „A posteriori error bound”

Autor: Grafiati
Data publikacji: 6 września 2023

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Rozprawy doktorskie na temat "A posteriori error bound"

1

Kunert, Gerd, Zoubida Mghazli, and Serge Nicaise. "A posteriori error estimation for a finite volume discretization on anisotropic meshes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601352.

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A singularly perturbed reaction diffusion problem is considered. The small diffusion coefficient generically leads to solutions with boundary layers. The problem is discretized by a vertex-centered finite volume method. The anisotropy of the solution is reflected by using \emph{anisotropic meshes} which can improve the accuracy of the discretization considerably. The main focus is on \emph{a posteriori} error estimation. A residual type error estimator is proposed and rigorously analysed. It is shown to be robust with respect to the small perturbation parameter. The estimator is also robust wi
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Rankin, Richard Andrew Robert. "Fully computable a posteriori error bounds for noncomforming and discontinuous galekin finite elemant approximation." Thesis, University of Strathclyde, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.501776.

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We obtain fully computable constant free a posteriori error bounds on the broken energy seminorm of the error in nonconforming and discontinuous Galerkin finite element approximations of a linear second ore elliptic problem on meshes omprised of triangular elements. We do this for nonconforming finite element approximations of uniform arbitrary order as well as for non-uniform order symmetric interior penalty Galerkin, non-symmetric interior penalty Galerkin and ncomplete interior penalty Galerkin finite element approximations.
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Merdon, Christian. "Aspects of guaranteed error control in computations for partial differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16818.

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Diese Arbeit behandelt garantierte Fehlerkontrolle für elliptische partielle Differentialgleichungen anhand des Poisson-Modellproblems, des Stokes-Problems und des Hindernisproblems. Hierzu werden garantierte obere Schranken für den Energiefehler zwischen exakter Lösung und diskreten Finite-Elemente-Approximationen erster Ordnung entwickelt. Ein verallgemeinerter Ansatz drückt den Energiefehler durch Dualnormen eines oder mehrerer Residuen aus. Hinzu kommen berechenbare Zusatzterme, wie Oszillationen der gegebenen Daten, mit expliziten Konstanten. Für die Abschätzung der Dualnormen der Resi
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Camacho, Fernando F. "A Posteriori Error Estimates for Surface Finite Element Methods." UKnowledge, 2014. http://uknowledge.uky.edu/math_etds/21.

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Problems involving the solution of partial differential equations over surfaces appear in many engineering and scientific applications. Some of those applications include crystal growth, fluid mechanics and computer graphics. Many times analytic solutions to such problems are not available. Numerical algorithms, such as Finite Element Methods, are used in practice to find approximate solutions in those cases. In this work we present L2 and pointwise a posteriori error estimates for Adaptive Surface Finite Elements solving the Laplace-Beltrami equation −△Γ u = f . The two sources of errors for
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5

Ainsworth, Mark. "A posteriori error estimation in the finite element method." Thesis, Durham University, 1989. http://etheses.dur.ac.uk/6326/.

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The work broadly consists of two parts. In the first part we construct a framework for analyzing and developing a posteriori error estimators for use in the finite element solution of elliptic partial differential equations which have smooth solutions. The analysis makes use of complementary variational principles and the superconvergence phenomenon associated with the finite element method. The second part generalizes these results to the important case when the solution of the boundary value problem contains singularities. It is shown how the classical techniques may be easily modified to pe
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Köhler, Karoline Sophie. "On efficient a posteriori error analysis for variational inequalities." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17635.

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Effiziente und zuverlässige a posteriori Fehlerabschätzungen sind eine Hauptzutat für die effiziente numerische Berechnung von Lösungen zu Variationsungleichungen durch die Finite-Elemente-Methode. Die vorliegende Arbeit untersucht zuverlässige und effiziente Fehlerabschätzungen für beliebige Finite-Elemente-Methoden und drei Variationsungleichungen, nämlich dem Hindernisproblem, dem Signorini Problem und dem Bingham Problem in zwei Raumdimensionen. Die Fehlerabschätzungen hängen vom zum Problem gehörenden Lagrange Multiplikator ab, der eine Verbindung zwischen der Variationsungleich
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Chow, Chak-On 1968. "On a posteriori finite element bound procedures for nonsymmetric Eigenvalue problems." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85266.

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Pled, Florent. "Vers une stratégie robuste et efficace pour le contrôle des calculs par éléments finis en ingénierie mécanique." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00776633.

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Ce travail de recherche vise à contribuer au développement de nouveaux outils d'estimation d'erreur globale et locale en ingénierie mécanique. Les estimateurs d'erreur globale étudiés reposent sur le concept d'erreur en relation de comportement à travers des techniques spécifiques de construction de champs admissibles, assurant l'aspect conservatif ou garanti de l'estimation. Une nouvelle méthode de construction de champs admissibles est mise en place et comparée à deux autres méthodes concurrentes, en matière de précision, coût de calcul et facilité d'implémentation dans les codes éléments fi
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Apel, Thomas, and Cornelia Pester. "Clément-type interpolation on spherical domains - interpolation error estimates and application to a posteriori error estimation." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601335.

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In this paper, a mixed boundary value problem for the Laplace-Beltrami operator is considered for spherical domains in $R^3$, i.e. for domains on the unit sphere. These domains are parametrized by spherical coordinates (\varphi, \theta), such that functions on the unit sphere are considered as functions in these coordinates. Careful investigation leads to the introduction of a proper finite element space corresponding to an isotropic triangulation of the underlying domain on the unit sphere. Error estimates are proven for a Clément-type interpolation operator, where appropriate, we
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10

Kunert, Gerd. "A posteriori error estimation for convection dominated problems on anisotropic meshes." Universitätsbibliothek Chemnitz, 2002. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200200255.

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A singularly perturbed convection-diffusion problem in two and three space dimensions is discretized using the streamline upwind Petrov Galerkin (SUPG) variant of the finite element method. The dominant convection frequently gives rise to solutions with layers; hence anisotropic finite elements can be applied advantageously. The main focus is on a posteriori energy norm error estimation that is robust in the perturbation parameter and with respect to the mesh anisotropy. A residual error estimator and a local problem error estimator are proposed and investigated. The analysis reveals that th
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