### 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(h^{1/2}) is demonstrated in the L^{2}(0, T; H^{1}(Ω)) norm, where h is the maximum diameter of a given triangulation.

Original language | English (US) |
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Pages (from-to) | 265-274 |

Number of pages | 10 |

Journal | Applied Mathematics & Optimization |

Volume | 8 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1982 |

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### ASJC Scopus subject areas

- Control and Optimization
- Applied Mathematics

### Cite this

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

Research output: Contribution to journal › Article

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 -