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Journal of Scientific Computing
Published in: Journal of Scientific Computing 2/2015

01-11-2015

A posteriori analysis of iterative algorithms for a nonlinear problem

Authors: Christine Bernardi, Jad Dakroub, Gihane Mansour, Toni Sayah

Published in: Journal of Scientific Computing | Issue 2/2015

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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 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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Metadata
Title
A posteriori analysis of iterative algorithms for a nonlinear problem
Authors
Christine Bernardi
Jad Dakroub
Gihane Mansour
Toni Sayah
Publication date
01-11-2015
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 2/2015
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-014-9980-4

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