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

Format:

Book

Author/Creator:

Verfürth, Rüdiger, author.

Series:

Numerical mathematics and scientific computation.

Numerical Mathematics and Scientific Computation

Language:

English

Subjects (All):

Error analysis (Mathematics).

Finite element method.

Physical Description:

1 online resource (534 p.)

Place of Publication:

Oxford : Oxford University Press, 2013.

Language Note:

English

Summary:

Self-adaptive discretization methods are now an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools in achieving this goal are a posteriori error estimates which give global and local information on the error of the numerical solution and which can easily be computed from the givennumerical solution and the data of the differential equation. This book reviews the most frequently used a posteriori

Contents:

Cover; Title Page; Copyright Page; 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-Coarsening2.3 Mesh-Smoothing; 2.4 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 Lp (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 Problems4.8 Mixed Formulation of the Poisson Equation; 4.9 The Equations of Linear Elasticity; 4.10 The Stokes Equations; 4.11 The Bi-harmonic Equation; 4.12 Non-Conforming Discretisations; 4.13 Convergence of the Adaptive Process II; 5 Nonlinear Elliptic Equations; 5.1 Abstract Nonlinear Problems; 5.2 Quasilinear Equations of Second Order; 5.3 Eigenvalue Problems Revisited; 5.4 The Stationary Navier-Stokes Equations; 6 Parabolic Equations; 6.1 The Heat Equation; 6.2 Time-Dependent Convection-Diffusion Equations; 6.3 Linear Parabolic Equations of Second Order

6.4 The Method of Characteristics6.5 The Time-Dependent Stokes Equations; 6.6 Nonlinear Parabolic Equations of Second Order; 6.7 Finite Volume Methods; 6.8 Convergence of the Adaptive Process III; References; List of Symbols; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-19-874348-3

1-299-39455-8

0-19-166877-X

0-19-166876-1

OCLC:

835161897