Convergent approximations in parabolic variational inequalities II: Hamilton-jacobi inequalities

Joseph W Jerome*

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper we consider two-sided parabolic inequalities of the form {Mathematical expression} {Mathematical expression} for all e in the convex support cone of the solution given by {Mathematical expression} {Mathematical expression} where {Mathematical expression} Such inequalities arise in the characterization of saddle-point payoffs u in two person differential games with stopping times as strategies. In this case, H is the Hamiltonian in the formulation. A numerical scheme for approximating u is obtained by the continuous time, piecewise linear, Galerkin approximation of a so-called penalized equation. A rate of convergence to u of order O(h1/2) is demonstrated in the L2(0, T; H1(Ω)) norm, where h is the maximum diameter of a given triangulation.

Original languageEnglish (US)
Pages (from-to)265-274
Number of pages10
JournalApplied Mathematics & Optimization
Volume8
Issue number1
DOIs
StatePublished - Jan 1 1982

Fingerprint

Parabolic Variational Inequalities
Hamiltonians
Hamilton-Jacobi
Triangulation
Cones
Approximation
Two-person Games
Stopping Time
Galerkin Approximation
T-norm
Differential Games
Saddlepoint
Piecewise Linear
Numerical Scheme
Continuous Time
Rate of Convergence
Cone
Formulation

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

Cite this

@article{78e576ff029446a69dc70baa65592693,
title = "Convergent approximations in parabolic variational inequalities II: Hamilton-jacobi inequalities",
abstract = "In this paper we consider two-sided parabolic inequalities of the form {Mathematical expression} {Mathematical expression} for all e in the convex support cone of the solution given by {Mathematical expression} {Mathematical expression} where {Mathematical expression} Such inequalities arise in the characterization of saddle-point payoffs u in two person differential games with stopping times as strategies. In this case, H is the Hamiltonian in the formulation. A numerical scheme for approximating u is obtained by the continuous time, piecewise linear, Galerkin approximation of a so-called penalized equation. A rate of convergence to u of order O(h1/2) is demonstrated in the L2(0, T; H1(Ω)) norm, where h is the maximum diameter of a given triangulation.",
author = "Jerome, {Joseph W}",
year = "1982",
month = "1",
day = "1",
doi = "10.1007/BF01447762",
language = "English (US)",
volume = "8",
pages = "265--274",
journal = "Applied Mathematics and Optimization",
issn = "0095-4616",
publisher = "Springer New York",
number = "1",

}

Convergent approximations in parabolic variational inequalities II : Hamilton-jacobi inequalities. / Jerome, Joseph W.

In: Applied Mathematics & Optimization, Vol. 8, No. 1, 01.01.1982, p. 265-274.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Convergent approximations in parabolic variational inequalities II

T2 - Hamilton-jacobi inequalities

AU - Jerome, Joseph W

PY - 1982/1/1

Y1 - 1982/1/1

N2 - In this paper we consider two-sided parabolic inequalities of the form {Mathematical expression} {Mathematical expression} for all e in the convex support cone of the solution given by {Mathematical expression} {Mathematical expression} where {Mathematical expression} Such inequalities arise in the characterization of saddle-point payoffs u in two person differential games with stopping times as strategies. In this case, H is the Hamiltonian in the formulation. A numerical scheme for approximating u is obtained by the continuous time, piecewise linear, Galerkin approximation of a so-called penalized equation. A rate of convergence to u of order O(h1/2) is demonstrated in the L2(0, T; H1(Ω)) norm, where h is the maximum diameter of a given triangulation.

AB - In this paper we consider two-sided parabolic inequalities of the form {Mathematical expression} {Mathematical expression} for all e in the convex support cone of the solution given by {Mathematical expression} {Mathematical expression} where {Mathematical expression} Such inequalities arise in the characterization of saddle-point payoffs u in two person differential games with stopping times as strategies. In this case, H is the Hamiltonian in the formulation. A numerical scheme for approximating u is obtained by the continuous time, piecewise linear, Galerkin approximation of a so-called penalized equation. A rate of convergence to u of order O(h1/2) is demonstrated in the L2(0, T; H1(Ω)) norm, where h is the maximum diameter of a given triangulation.

UR - http://www.scopus.com/inward/record.url?scp=0742301914&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0742301914&partnerID=8YFLogxK

U2 - 10.1007/BF01447762

DO - 10.1007/BF01447762

M3 - Article

AN - SCOPUS:0742301914

VL - 8

SP - 265

EP - 274

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

SN - 0095-4616

IS - 1

ER -