A feedback element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimator

Keywords

Finite element method, Estimator, Mathematics, Mixed finite element method, A priori and a posteriori

References

• Feedback Systems and Adaptivity for Numerical Computations.Werner C. Rheinboldt — 1983
• Reliable error estimation and mesh adaptation for the finite element methodIvo Babuška, Werner C. Rheinboldt — 1979
• Error Estimates for Adaptive Finite Element ComputationsI. Babuvška, Werner C. Rheinboldt — 1978
• Some a posteriori error estimators for elliptic partial differential equationsRandolph E. Bank, A. Weiser — 1985
• Factors influencing output non-linearity error of a high-precision load sensor and the error calculationWie Fuyu, Fang Mannan — 1987
• Feedback and adaptive finite element solution of one-dimensional boundary value problemsI. Bubuška, Michael Vogelius — 1984
• Geometrically nonlinear analysis of layerwise anisotropic shell structures by hybrid strain based lower order elementsC.W.S. To, M.L. Liu — 1987
• Asymptotically exact a posteriori error estimator for biquadratic elementsIvo Babuška, Dehao Yu — 1987
• Adaptive Methods and Error Estimation for Elliptic Problems of Structural Mechanics.I. Babuska, A. Miller, M. Vogelius — 1983

Cited by

• Recovery type a posteriori error estimates in finite element methodsZhimin Zhang, Ningning Yan — 2001
• Numerical aspects of computational homogenizationMarta Serafin, Witold Cecot — 2013
• Gradient recovery type a posteriori error estimate for finite element approximation on non-uniform meshesLiu Du, Ningning Yan — 2001
• Adaptive modeling of plate structuresUroš Bohinc — 2011
• A Posteriori Error Estimators of Gradient Recovery Type for Fem of a Model Optimal Control ProblemNingning Yan — 2003
• Removing the saturation assumption in a posteriori error analysisRicardo H. Nochetto — 1993
• Sharp Error Bounds for Piecewise Polynomial Approximation: Revisit and Application to Elliptic PDE Eigenvalue ComputationHehu Xie, Zhimin Zhang — 2015
• Encadrement a posteriori de quantités locales dans les problèmes de viscoélaticité linéaire résolus par la méthode des éléments finisLudovic Chamoin — 2007
• DECAY CHARACTERISTICS OF THE HAT INTERPOLATION WAVELET COEFFICIENTS IN THE TWO-DIMENSIONAL MULTIRESOLUTION REPRESENTATIONKiwoon Kwon, Yoon Young Kim — 2005
• A posteriori error estimators for nonconforming finite element methodsEnzo A. Dari, Ricardo G. Durán, Claudio Padra — 1996
• Vérification des facteurs d'intensité de contrainte calculés par XFEMJulien Panetier — 2009
• Milestones of Direct Variational Calculus and its Analysis from the 17th Century until today and beyond – Mathematics meets Mechanics – with restriction to linear elasticityErwin Stein — 2012
• A POSTERIORI ERROR ESTIMATES OF FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS陈艳萍 — 1999
• Finite Element Analysis of Acoustic ScatteringFrank Ihlenburg — 1998
• Convergence of adaptive hybridizable discontinuous Galerkin methods for second-order elliptic equationsWujun Zhang — 2012
• An experimental survey of a posteriori Courant finite element error control for the Poisson equationCarsten Carstensen, Sören Bartels, Roland Klose — 2001
• A PDE approach to numerical fractional diffusionEnrique Otarola Pasten — 2015
• Adaptive tetrahedral mesh generation by constrained centroidal voronoi‐delaunay tessellations for finite element methodsJie Chen, Yunqing Huang, Desheng Wang — 2014
• Cartesian grid FEM (cgFEM): High performance h-adaptive FE analysis with efficient error control. Application to structural shape optimizationEnrique Nadal Soriano — 2014
• Constant‐free explicit error estimator with sharp upper error bound property for adaptive FE analysis in elasticity and fractureTymofiy Gerasimov, E. Stein, Peter Wriggers — 2015

Related papers

• Finite element analysis: theory and practiceMaurice J. Fagan — 1992
• A finite-element method for simulating unstable two-phase flowSantanu Khataniar, Ekwere J. Peters — 1990
• High Accuracy Finite Element Method of Structural Dynamic AnalysisXiujuan Cao — 2006
• Moving particle finite element method with global smoothnessSu Hao, Wing Kam Liu, Ted Belytschko — 2004
• Comparative Analysis of the Adaptive Generalized Finite Element Method and the Finite Element Method for Free Vibration of BarsMarcos Arndt, Roberto Dalledone Machado, A. Scremin — 2010
• Study on three-dimensional finite element numerical simulationYou Guang-fen — 2009
• A Comparison between Finite Volume Method and Finite Element MethodJiahui Sun — 2011
• Finite Element Interpolating Post-ProcessingYi Wang — 2002
• A HIGHER-ORDER NONSTANDARD FINITE ELEMENT METHOD FOR ONE-DIMENSIONAL ELLIPTIC PROBLEMSZhilin Li — 2021
• Finite Element ProceduresKlaus‐Jürgen Bathe — 1995