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

Joseph W. Jerome*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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
Issue number1
StatePublished - Jan 1982

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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