Approximation Schemes for Monotone Systems of Nonlinear Second Order Partial Differential Equations: Convergence Result and Error Estimate

Ariela Briani; Fabio Camilli; Hasnaa Zidani

inria-00627520, version 1

Approximation Schemes for Monotone Systems of Nonlinear Second Order Partial Differential Equations: Convergence Result and Error Estimate

Ariela Briani () ^1, 2, Fabio Camilli ³, Hasnaa Zidani ()^a^, 1, 4

Differential Equations and Applications 4 (2012) 297-317

Abstract: We consider approximation schemes for monotone systems of fully nonlinear second order partial di erential equations. We rst prove a general convergence result for monotone, consistent and regular schemes. This result is a generalization to the well known framework of Barles-Souganidis, in the case of scalar nonlinear equation. Our second main result provides the convergence rate of approximation schemes for weakly coupled systems of Hamilton-Jacobi-Bellman equations. Examples including nite di erence schemes and Semi-Lagrangian schemes are discussed.

a – Ecole Nationale Supérieure de Technique Avancée
1: Unité de Mathématiques Appliquées (UMA)
ENSTA ParisTech
2: Laboratoire de Mathématiques et Physique Théorique (LMPT)
CNRS : UMR6083 – Université François Rabelais - Tours
3: Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate (MeMoMat)
Universita di Roma "La Sapienza"
4: COMMANDS (INRIA Saclay - Ile de France)
INRIA – CNRS : UMR7641 – Polytechnique - X – ENSTA ParisTech

inria-00627520, version 1
http://hal.inria.fr/inria-00627520
oai:hal.inria.fr:inria-00627520
From: Estelle Bouzat <>
Submitted on: Wednesday, 28 September 2011 18:50:22
Updated on: Thursday, 21 June 2012 16:25:55

See detailed view

Associated documents

PDF :

DOI: 10.7153/dea-04-18

Export

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Articles in peer-reviewed journal</head>
<biblStruct type="article" xml:id="inria-00627520"><analytic>
<author><persName><forename>Ariela</forename><surname>Briani</surname></persName>
<affiliation>
<orgName type="laboratory">UMA</orgName>
<orgName type="team">Unité de Mathématiques Appliquées</orgName>
<country>FR</country>
<orgName type="institution">ENSTA ParisTech</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">LMPT</orgName>
<orgName type="team">Laboratoire de Mathématiques et Physique Théorique</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR6083</orgName>
<orgName type="institution">Université François Rabelais - Tours</orgName>
</affiliation>
</author>
<author><persName><forename>Fabio</forename><surname>Camilli</surname></persName>
<affiliation>
<orgName type="laboratory">MeMoMat</orgName>
<orgName type="team">Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate</orgName>
<country>IT</country>
<orgName type="institution">Universita di Roma "La Sapienza"</orgName>
</affiliation>
</author>
<author><persName><forename>Hasnaa</forename><surname>Zidani</surname></persName>
<affiliation>
<orgName type="laboratory">UMA</orgName>
<orgName type="team">Unité de Mathématiques Appliquées</orgName>
<country>FR</country>
<orgName type="institution">ENSTA ParisTech</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">INRIA Saclay - Ile de France</orgName>
<orgName type="team">COMMANDS</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">CNRS : UMR7641</orgName>
<orgName type="institution">Polytechnique - X</orgName>
<orgName type="institution">ENSTA ParisTech</orgName>
</affiliation>
</author>
<title type="main" level="a">Approximation Schemes for Monotone Systems of Nonlinear Second Order Partial Differential Equations: Convergence Result and Error Estimate</title></analytic><monogr><title level="j" type="main">Differential Equations and Applications</title><imprint><publisher>Ele-Math</publisher><biblScope type="publicationDate">2012-00-00</biblScope><biblScope type="vol">4</biblScope><biblScope type="pp">297-317</biblScope></imprint></monogr><idno type="doi">10.7153/dea-04-18</idno><idno type="HALid">http://hal.inria.fr/inria-00627520</idno><idno type="HALFile">http://hal.inria.fr/inria-00627520/PDF/briani_camilli_zidani_finalversion.pdf</idno></biblStruct>
</listBibl>
</listBibl>