Newton- LL ∗ method for the second-order semi-linear elliptic partial differential equations

Eunjung Lee

doi:10.1016/j.camwa.2014.11.006

Newton- LL ^∗ method for the second-order semi-linear elliptic partial differential equations

Eunjung Lee

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Newton's method with first-order system least squares (FOSLS) finite element method has been widely used to approximately solve a system of nonlinear partial differential equations (Adler et al., 2010 [9], Codd et al., 2003 [10], Manteuffel et al., 2006 [11]). In this paper, we propose to use the first order system LL^∗ method to find a correction in each Newton's iteration which provides an ^L2-approximation of the second-order semi-linear elliptic partial differential equations while the typical Newton-FOSLS method provides^H1-approximations. The numerical tests have been conducted to validate the theory.

Original language	English
Pages (from-to)	1031-1044
Number of pages	14
Journal	Computers and Mathematics with Applications
Volume	69
Issue number	10
DOIs	https://doi.org/10.1016/j.camwa.2014.11.006
Publication status	Published - 2015 May 1

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2013004836 ).

Publisher Copyright:
© 2014 Elsevier Ltd. All rights reserved.

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

Access to Document

10.1016/j.camwa.2014.11.006

Cite this

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title = "Newton- LL ∗ method for the second-order semi-linear elliptic partial differential equations",

abstract = "Newton's method with first-order system least squares (FOSLS) finite element method has been widely used to approximately solve a system of nonlinear partial differential equations (Adler et al., 2010 [9], Codd et al., 2003 [10], Manteuffel et al., 2006 [11]). In this paper, we propose to use the first order system LL∗ method to find a correction in each Newton's iteration which provides an L2-approximation of the second-order semi-linear elliptic partial differential equations while the typical Newton-FOSLS method providesH1-approximations. The numerical tests have been conducted to validate the theory.",

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