Automated Goal-Oriented Error Control I: Stationary Variational Problems

This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the linearized dual problem, automated derivation and evaluation...

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Published inSIAM journal on scientific computing Vol. 35; no. 3; pp. C173 - C193
Main Authors Rognes, Marie E, Logg, Anders
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects
A posteriori
Adaptivity
Algorithms
Approximation
Automated
Automation
Discretization
Dual problem
Error control
Errors
Estimates
Finite element method
Laboratories
Mathematical analysis
Mathematical functions
Mathematical models
Nonlinear
Nonlinearity
Poisson equation
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Abstract This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the linearized dual problem, automated derivation and evaluation of a posteriori error estimates, and automated adaptive mesh refinement to control the error in a given goal functional to within a given tolerance. Numerical examples representing a variety of different discretizations of linear and nonlinear partial differential equations are presented, including Poisson's equation, a mixed formulation of linear elasticity, and the incompressible Navier--Stokes equations. [PUBLICATION ABSTRACT]
AbstractList This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the linearized dual problem, automated derivation and evaluation of a posteriori error estimates, and automated adaptive mesh refinement to control the error in a given goal functional to within a given tolerance. Numerical examples representing a variety of different discretizations of linear and nonlinear partial differential equations are presented, including Poisson's equation, a mixed formulation of linear elasticity, and the incompressible Navier--Stokes equations.
This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the linearized dual problem, automated derivation and evaluation of a posteriori error estimates, and automated adaptive mesh refinement to control the error in a given goal functional to within a given tolerance. Numerical examples representing a variety of different discretizations of linear and nonlinear partial differential equations are presented, including Poisson's equation, a mixed formulation of linear elasticity, and the incompressible Navier--Stokes equations. [PUBLICATION ABSTRACT]
This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the linearized dual problem, automated derivation and evaluation of a posteriori error estimates, and automated adaptive mesh refinement to control the error in a given goal functional to within a given tolerance. Numerical examples representing a variety of different discretizations of linear and nonlinear partial differential equations are presented, including Poisson's equation, a mixed formulation of linear elasticity, and the incompressible Navier- Stokes equations. © 2013 Society for Industrial and Applied Mathematics.
Author Rognes, Marie E
Logg, Anders
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BackLink https://research.chalmers.se/publication/191173$$DView record from Swedish Publication Index
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SubjectTerms A posteriori
Adaptivity
Algorithms
Approximation
Automated
Automation
Discretization
Dual problem
Error control
Errors
Estimates
Finite element method
Laboratories
Mathematical analysis
Mathematical functions
Mathematical models
Nonlinear
Nonlinearity
Poisson equation
Title Automated Goal-Oriented Error Control I: Stationary Variational Problems
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