Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities | Zendy

Klaus Deckelnick | Zendy; Charles M. Elliott | Zendy

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Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities

Author(s) -

Klaus Deckelnick,

Charles M. Elliott

Publication year - 2004

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/103

Subject(s) - hamilton–jacobi equation , classification of discontinuities , uniqueness , eikonal equation , monotone polygon , mathematics , viscosity solution , class (philosophy) , regular polygon , mathematical analysis , error analysis , pure mathematics , viscosity , physics , computer science , geometry , quantum mechanics , artificial intelligence

H(ru) = f(x), x 2 , where H is convex and f is allowed to be discontinuous. Under a suitable assumption on f we prove a comparison principle for viscosity sub- and supersolutions in the sense of Ishii. Furthermore, we develop an error analysis for a class of finite difference schemes, which are monotone, consistent and satisfy a suitable stability condition.

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