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Table of contents for The finite element method and its reliability / Ivo Babuska and Theofanis Strouboulis.




1  Introduction
1.0  Introduction
1.1  A brief history of the finite element method
1.2  On computational engineering
2  Mathematical formulation of the model problem
2.0  Introduction
2.1  The one-dimensional model problem
2.1*  The two-dimensional model problem
2.2  The variational formulation of the model problem
2.2*  The variational formulation of the model problem in two dimensions
2.3  Smoothness of the solution of the model problem
2.3*  Smoothness of the solution of the two-dimensional model problem
2.4  Historical and bibliographical remarks
3  The finite element method
3.0  Introduction
3.1  The Galerkin method and the properties of the approximate solution
3.1*  The Galerkin method in two dimensions
3.2  The finite element method
3.2*  The finite element method in two dimensions
3.3  The finite element interpolation and approximation error
3.3*  The finite element interpolation and approximation error in
two dimensions
3.4  The finite element interpolation and approximation: a special case
3.4*  The interpolation error for the function ragp(0) in two dimensions
3.5  The description of the mesh and analyses of its optimality
3.5*  The description of the mesh and analysis of its optimality in
two dimensions
3.6  Historical and bibliographical comments
4  Local behavior in the finite element method
4.0  Introduction
4.1  A-priori estimates for the nodal errors and the maximum error
4.1* A-priori estimates for the nodal errors and the maximum error in
two dimensions
4.2  A-priori estimates for negative norms of the error
4.2*  A-priori estimates for negative norms of the error in two dimensions
4.3  Local and pollution error in the finite element solution
4.3* The splitting of the error in the two-dimensional case
4.4  A-priori estimates for the pollution error
4.4* A-priori estimates for the pollution error in two dimensions
4.5  Further analysis of the pollution error: Interior estimates
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4.5*  The interior estimates in two dimensions
4.6  A-priori estimates for the local error: superconvergence
4.6*  Superconvergence in two dimensions
4.7  A general approach for the analysis of local behavior of finite
element methods for locally periodic meshes and its applications
4.7* A general approach for local asymptotic analysis and analysis of
the superconvergence in two dimensions
4.8   Superconvergence via local averaging
4.8*  Superconvergence based on local recovery: the two-dimensional case
4.9  Historical and bibliographical comments
5  A-posteriori estimation of the error
5.0  Introduction
5.1  The residuum and the construction of lower and upper estimators
for the energy norm of the error
5.1*  The residuum and the construction of lower and upper estimators
for the energy norm of the error: the two dimensional case
5.2  Analysis of the Dirichlet element residual estimator
5.2*  Analysis of the Dirichlet element residual estimator in two dimensions
5.3  Analysis of the Neumann element residual estimator
5.3*  Analysis of the Neumann element residual estimator in two
dimensions
5.4  Subdomain residual estimates
5.4*  Subdomain residual estimates in two dimensions
5.5  Analysis of the explicit element residual estimator
5.5*  Analysis of the explicit element residual estimator in two dimensions
5.6  A-posteriori error estimates based on local averaging
5.6*  A-posteriori estimates based on local averaging: the
two-dimensional case
5.7  The effectivity of the error indicators: the principles for their
comparison and the detailed analysis of their quality
5.7*  The asymptotic analysis of the effectiveness of the element error
indicators in two dimensions
5.8  Historical and bibliographical comments
6 Guaranteed a-posteriori error estimation and a-posteriori
estimation of the pollution error
6.0  Introduction
6.1  Upper and lower bounds for the energy norm of the error
6.1*  Upper and lower bounds for the energy norm of the error in
two dimensions
6.2  Upper and lower bounds for the error in the output, and
a-posteriori estimation of the pollution
6.2*  Upper and lower bounds for the error in the outputs, and
a-posteriori estimation of the pollution error in two dimensions
6.3*  Historical and bibliographical comments
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.epilogue
/ Appendix to chapter 2
Appendix to chapter 3
Glossary of symbols
Author Index
Subject Index