Explicit Residual Methods

Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

Numerical methods are now well established for the approximation of the solution to partial differential equations. These simulations allow to better understand complex phenomenon and lead to their control and optimization. The accuracy of the solution needs nevertheless be certified and in some case improved and the measurement of the error between the exact solution to the problem and the approximated one provided by the computer simulation must be estimated. A large amount of research has been done in this direction. This paper summarizes some of the most classical approaches that are available and allow, at very little extra computational cost to certify the results. These are known as the explicit residual techniques.

Keywords

A posteriori error estimation Explicit residual techniques Numerical convergence Finite element method Reduced basis approximation 

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis Lions, CNRS, Institut Universitaire de FranceSorbonne Universités, UPMC Univ Paris 06, Univ. Paris Diderot, Sorbonne Paris CitéParisFrance
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

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