Data Oscillation and Convergence of Adaptive FEM

By Pedro Morin, Ricardo H. Nochetto, Kunibert G. Siebert. SIAM Journal on Numerical Analysis, 2000

571 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8bd6b2d2e43caabaac969641e6d23abc0fba3862

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In Computational Mechanics

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Citations in the corpus

A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems (2003, methodology): “In this study, for simplicity reasons, we are not considering the effect of data oscillations as in [15].”
Approximation of high-dimensional parametric PDEs * (2015, background): “Let us point out that a similar objective can be attained when considering the spatial discretization of a single PDE, by either adaptive wavelet methods [21, 22, 38] or by adaptive finite element methods [70, 7, 86].”
Adaptive stochastic Galerkin FEM (2014, methodology): “It may be useful to mark additional elements of T0 for refinement based on unresolved components of f ; we refer to [20] for details.”
Approximation Classes for Adaptive Methods (2002, background): “For example, the papers of D¨orfler [10] and Morin, Nochetto, and Siebert [ 13 ] prove the convergence of certain AFEMs which use piecewise linear approximation on partitions adaptively generated using newest vertex bisection (see §2 for a discussion of newest vertex bisection).”
Convergence Analysis of an Adaptive Finite Element Method for Distributed Control Problems with Control Constraints (2007, methodology): “AFEMs typically consist of successive loops of the sequence SOLVE → ESTIMATE → MARK → REFINE .”
Primer of Adaptive Finite Element Methods (2011, methodology): “We refer to [7, 9, 16, 17, 23, 24, 37, 40–42] for other approaches and to Sect.”
Design of Adaptive Finite Element Software - The Finite Element Toolbox ALBERTA (2005, methodology): “Bremen and Augsburg, October 2004 Alfred Schmidt and Kunibert G. Siebert Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .”
AN A POSTERIORI ERROR ANALYSIS OF ADAPTIVE FINITE ELEMENT METHODS FOR DISTRIBUTED ELLIPTIC CONTROL PROBLEMS WITH CONTROL CONSTRAINTS (2008, methodology): “The adaptive refinement process The refinement of the triangulation Th(Ω) is based on a bulk criterion that has been previously used in the convergence analysis of adaptive finite element for nodal finite element methods [8,13,25] and for nonconforming,”
Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method (2008, unknown): “, |||u− Uk|||Ω = |||u− Uk+1|||Ω; see [17, 18] for further details.”
Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs (2011, methodology): “We should point out that a similar program was developed when solving a single PDE by either adaptive wavelet methods [7,8,14] or by adaptive finite element methods [4,12,21,26].”
Adaptive Finite Element Methods with convergence rates (2004, methodology): “But we want to conform exactly to the algorithm in [17] so that we do not have to detour through a new development of a posteriori error analysis in this modified setting.”
Reliability and efficiency of an anisotropic zienkiewicz-zhu error estimator (2006, methodology): “Then we replace the data f and g, usually not exactly integrable, by suitable functions fK and gE, piecewise constant with respect to Th and Eh,N , respectively [29, 36].”
Theory of adaptive finite element methods: An introduction (2009, methodology): “R. H. Nochetto, K. G. Siebert, and A. Veeser”