Yamamoto's principle and its applications to precise finite element error analysis

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(02)00727-6 ◽

2003 ◽

Vol 152 (1-2) ◽

pp. 507-532 ◽

Author(s):

Takuya Tsuchiya ◽

Kazuki Yoshida ◽

Sae Ishioka

Keyword(s):

Finite Element ◽

Error Analysis ◽

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Finite Element Error Analysis Approach for Three-Dimensional Incompressible Viscous Fluid Flow Analysis

International Journal of Computational Fluid Dynamics ◽

10.1080/10618569908940836 ◽

1999 ◽

Vol 12 (3-4) ◽

pp. 323-330 ◽

Author(s):

Y. MATSUDA ◽

C. SHAO ◽

K. MATSUMOTO ◽

H. FUJITA ◽

I. ICHIKAWA

Keyword(s):

Finite Element ◽

Viscous Fluid ◽

Error Analysis ◽

Flow Analysis ◽

Three Dimensional ◽

Incompressible Viscous Fluid ◽

Viscous Fluid Flow ◽

Fluid Flow Analysis ◽

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Finite element error analysis of a time-fractional nonlocal diffusion equation with the Dirichlet energy

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.113066 ◽

2021 ◽

Vol 382 ◽

pp. 113066 ◽

Author(s):

J. Manimaran ◽

L. Shangerganesh ◽

Amar Debbouche

Keyword(s):

Finite Element ◽

Diffusion Equation ◽

Error Analysis ◽

Nonlocal Diffusion ◽

Dirichlet Energy ◽

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Finite element error analysis for a projection-based variational multiscale method with nonlinear eddy viscosity

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2008.03.015 ◽

2008 ◽

Vol 344 (2) ◽

pp. 627-641 ◽

Author(s):

V. John ◽

S. Kaya ◽

A. Kindl

Keyword(s):

Finite Element ◽

Error Analysis ◽

Eddy Viscosity ◽

Multiscale Method ◽

Variational Multiscale Method ◽

Variational Multiscale ◽

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Some remarks on the history and future of averaging techniques in a posteriori finite element error analysis

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik ◽

10.1002/zamm.200410101 ◽

2004 ◽

Vol 84 (1) ◽

pp. 3-21 ◽

Author(s):

C. Carstensen

Keyword(s):

Finite Element ◽

Error Analysis ◽

A Posteriori ◽

Element Error ◽

Averaging Techniques

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A tutorial in elementary finite element error analysis: A systematic presentation of a priori and a posteriori error estimates

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/s0045-7825(97)00230-2 ◽

1998 ◽

Vol 158 (1-2) ◽

pp. 1-22 ◽

Author(s):

James R Stewart ◽

Thomas J.R Hughes

Keyword(s):

Finite Element ◽

Error Analysis ◽

Error Estimates ◽

A Priori ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

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Adaptive Grid Design for Finite Element Analysis In Optimization: Part 1, Review of Finite Element Error Analysis

Computer Aided Optimal Design: Structural and Mechanical Systems ◽

10.1007/978-3-642-83051-8_14 ◽

1987 ◽

pp. 493-562 ◽

Author(s):

Noboru Kikuchi

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Error Analysis ◽

Adaptive Grid ◽

Element Analysis ◽

Grid Design ◽

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Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis

Numerische Mathematik ◽

10.1007/s00211-004-0548-3 ◽

2004 ◽

Vol 99 (1) ◽

pp. 1-24 ◽

Author(s):

S. Bartels ◽

C. Carstensen ◽

G. Dolzmann

Keyword(s):

Finite Element ◽

Error Analysis ◽

A Priori ◽

A Posteriori ◽

Dirichlet Conditions ◽

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Global Stabilization of BBM–Burgers’ Type Equations by Nonlinear Boundary Feedback Control Laws: Theory and Finite Element Error Analysis

Journal of Scientific Computing ◽

10.1007/s10915-019-01039-5 ◽

2019 ◽

Vol 81 (2) ◽

pp. 845-880 ◽

Author(s):

Sudeep Kundu ◽

Amiya Kumar Pani

Keyword(s):

Finite Element ◽

Feedback Control ◽

Error Analysis ◽

Nonlinear Boundary ◽

Global Stabilization ◽

Control Laws ◽

Boundary Feedback Control ◽

Burgers Type Equations ◽

Element Error ◽

Nonlinear Boundary Feedback

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Helmholtz decomposition of vector fields with mixed boundary conditions and an application to a posteriori finite element error analysis of the Maxwell system

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.3104 ◽

2014 ◽

Vol 38 (4) ◽

pp. 738-750 ◽

Author(s):

Emmanuel Creusé ◽

Serge Nicaise ◽

Zuqi Tang

Keyword(s):

Finite Element ◽

Error Analysis ◽

Boundary Conditions ◽

Vector Fields ◽

Mixed Boundary ◽

Mixed Boundary Conditions ◽

Helmholtz Decomposition ◽

Maxwell System ◽

A Posteriori ◽

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Higher order two-scale finite element error analysis for thermoelastic problem in quasi-periodic perforated structure

International Journal of Modern Physics C ◽

10.1142/s0129183117500978 ◽

2017 ◽

Vol 28 (07) ◽

pp. 1750097

Author(s):

Mingxiang Deng ◽

Yongping Feng

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Error Analysis ◽

Thermal Behavior ◽

Higher Order ◽

Numerical Results ◽

Thermoelastic Problem ◽

Asymptotic Expressions ◽

Element Error ◽

In this paper, one new coupled higher order two-scale finite element method (TSFEM) for thermoelastic problem in composites is proposed. Firstly, some new two-scale asymptotic expressions and homogenization formulations for the problem are briefly given. Next, some high–low coupled approximate errors corresponding to TSFEM are analyzed. Finally, some numerical results of the displacement and the increment of temperature are presented, which show that TSFEM is an effective method for predicting the mechanical and the thermal behavior of composites in quasi-periodic perforated structure.

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