### 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) |
---|---|

Pages (from-to) | 265-274 |

Number of pages | 10 |

Journal | Applied Mathematics & Optimization |

Volume | 8 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 1982 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Optimization
- Applied Mathematics