Local Error Estimates for Discontinuous Solutions of Nonlinear Hyperbolic Equations | Zendy

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Local Error Estimates for Discontinuous Solutions of Nonlinear Hyperbolic Equations

Author(s) -

Eitan Tadmor

Publication year - 1991

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/0728048

Subject(s) - mathematics , pointwise , conservation law , mathematical analysis , nonlinear system , hyperbolic partial differential equation , viscosity solution , regularization (linguistics) , scalar (mathematics) , partial differential equation , physics , geometry , quantum mechanics , artificial intelligence , computer science

. Let u(x; t) be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smoothinitial data. Suppose u " (x; t) is the solution of an approximate viscosity regularization, where " ? 0 is the small viscosityamplitude. We show that by post-processing the small viscosity approximation u " , we can recover pointwise values of u and itsderivatives with an error as close to " as desired.The analysis relies on the adjoint problem of the forward error equation, which ...

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