A posteriori error estimation techniques for finite element methods

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A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This text gives a unified approach to these techniques and guides graduate students, researchers, and practitioners towards understanding, applying and developing self-adaptive discretization methods.

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Title Statements

Full title :A posteriori error estimation techniques for finite element methods / Rüdiger Verfürth.

Summary

Edition Statements

Publication Date:2013.

Publication Statements

Publisher(s):Oxford University Press
Place of Publication:Oxford, UK
Language:eng
Publication Date:2013.

The Physical Object

Description:1 online resource (xviii, 393 pages)

Edition Identifiers

ISBN:9780191668760, 0191668761, 9780191668777, 019166877X, 9780191758485, 0191758485, 0198743483, 9780198743484, 1299394558, 9781299394551
oclc:ocn835161897
LC Classification:QC20.7.F56
Dewey Decimal:518/.25

Cover; Contents; 1 A Simple Model Problem; 1.1 Motivation and Overview; 1.2 The Model Problem and its Discretisation; 1.3 Notations and Auxiliary Results; 1.4 Residual Estimates; 1.5 A Vertex-Oriented Residual Error Indicator; 1.6 Edge Residuals; 1.7 Auxiliary Local Problems; 1.8 A Hierarchical Approach; 1.9 Gradient Recovery; 1.10 Equilibrated Residuals; 1.11 Dual Weighted Residuals; 1.12 The Hyper-Circle Method; 1.13 Efficiency and Asymptotic Exactness; 1.14 Convergence of the Adaptive Process I; 1.15 Summary and Outlook; 2 Implementation; 2.1 Mesh-Refinement; 2.2 Mesh-Coarsening.

2.3 Mesh-Smoothing2.4 Data Structures; 2.5 Numerical Examples; 3 Auxiliary Results; 3.1 Function Spaces; 3.2 Finite Element Meshes and Spaces; 3.3 Trace Inequalities; 3.4 Poincaré and Friedrichs' Inequalities; 3.5 Interpolation Error Estimates; 3.6 Inverse Estimates; 3.7 Decomposition of Affine Functions in L[sup(p)] (0, 1; Y*); 3.8 Estimation of Residuals; 4 Linear Elliptic Equations; 4.1 Abstract Linear Problems; 4.2 The Model Problem Revisited; 4.3 Reaction-Diffusion Equations; 4.4 Convection-Diffusion Equations; 4.5 Anisotropic Meshes; 4.6 Non-Smooth Coefficients; 4.7 Eigenvalue Problems.

4.8 Mix…