L∞- error estimate for nonlinear HJB equations

Messaoud Boulbrachene

doi:10.12988/ijma.2015.5237

L∞- error estimate for nonlinear HJB equations

Messaoud Boulbrachene^*

^*Corresponding author for this work

Mathematics

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

Abstract

This paper is concerned with the standard finite element approximation of Hamilton-Jacobi-Bellman Equations (HJB) with nonlinear source terms. Under a realistic condition on the nonlinearity, we characterize the discrete solution as a fixed point of a contraction. As a result of this, we also derive a sharp L∞- error estimate of the approximation.

Original language	English
Pages (from-to)	1255-1259
Number of pages	5
Journal	International Journal of Mathematical Analysis
Volume	9
Issue number	25-28
DOIs	https://doi.org/10.12988/ijma.2015.5237
Publication status	Published - 2015

Keywords

Contraction
Finite elements
Fixed point
HJB equations
L∞ error estimates
Quasi-variational inequalities

ASJC Scopus subject areas

General Mathematics

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10.12988/ijma.2015.5237

Cite this

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abstract = "This paper is concerned with the standard finite element approximation of Hamilton-Jacobi-Bellman Equations (HJB) with nonlinear source terms. Under a realistic condition on the nonlinearity, we characterize the discrete solution as a fixed point of a contraction. As a result of this, we also derive a sharp L∞- error estimate of the approximation.",

keywords = "Contraction, Finite elements, Fixed point, HJB equations, L∞ error estimates, Quasi-variational inequalities",

author = "Messaoud Boulbrachene",

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AB - This paper is concerned with the standard finite element approximation of Hamilton-Jacobi-Bellman Equations (HJB) with nonlinear source terms. Under a realistic condition on the nonlinearity, we characterize the discrete solution as a fixed point of a contraction. As a result of this, we also derive a sharp L∞- error estimate of the approximation.

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KW - L∞ error estimates

KW - Quasi-variational inequalities

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L∞- error estimate for nonlinear HJB equations

Abstract

Keywords

ASJC Scopus subject areas

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