The convergence rate of finite difference schemes in the presence of shocks

• : Finite difference approximations generically have O(1) pointwise errors close to a shock. We show that this local error may effect the smooth part of the solution such that only first order is achieved even for formally higher-order methods. Analytic and numerical examples of this form of accuracy are given. We also show that a converging method will have the formal order of accuracy in domains where no characteristics have passed through a shock.

Subject headings

NATURVETENSKAP  -- Data- och informationsvetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences (hsv//eng)

Keyword

finite difference approximation; shock wave; hyperbolic system

Publication and Content Type

ref (subject category)

art (subject category)