A POSTERIORI ANALYSIS OF ITERATIVE ALGORITHMS FOR A NONLINEAR PROBLEM - Sorbonne Université Access content directly
Preprints, Working Papers, ... Year : 2013

A POSTERIORI ANALYSIS OF ITERATIVE ALGORITHMS FOR A NONLINEAR PROBLEM

Abstract

A posteriori error indicators have been studied in recent years owing to their remarkable capacity to enhance both speed and accuracy in computing. This work deals with a posteriori error estimation for the finite element discretization of a nonlinear problem. For a given nonlinear equation considering finite elements we solve the discrete problem using two iterative methods involving some kind of linearization. For each of them, there are actually two sources of error, namely discretization and linearization. Balancing these two errors can be very important, since it avoids performing an excessive number of iterations. Our results lead to the construction of computable upper indicators for the full error. Several numerical tests are provided to evaluate the efficiency of our indicators.
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Dates and versions

hal-00918226 , version 1 (13-12-2013)
hal-00918226 , version 2 (18-12-2013)

Identifiers

  • HAL Id : hal-00918226 , version 2

Cite

Christine Bernardi, Jad Dakroub, Gihane Mansour, Toni Sayah. A POSTERIORI ANALYSIS OF ITERATIVE ALGORITHMS FOR A NONLINEAR PROBLEM. 2013. ⟨hal-00918226v2⟩
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