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Approximation schemes for viscosity solutions of Hamilton-Jacobi equations. (English) Zbl 0536.70020

Equations of Hamilton-Jacobi type arise in many areas of application, including the calculus of variations, control theory and differential games. Recently M. G. Crandall and P. L. Lions established the correct notion of generalized solutions for these equations [C. R. Acad. Sci. Paris, Ser. I 292, 183-186 (1981; Zbl 0469.49023)]. This article discusses the convergence of general approximation schemes to this solution and gives, under certain hypotheses, explicit error estimates. These results are then applied to obtain various representations as limits of solutions of general explicit and implicit finite difference schemes, with error estimates.

MSC:

70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
70-08 Computational methods for problems pertaining to mechanics of particles and systems
49L99 Hamilton-Jacobi theories

Citations:

Zbl 0469.49023
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References:

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