### Riemann problem

(consequence of discontinuities in numerical methods)

A **Riemann problem** is a type of "subproblem" that occurs
when solving equations including discontinuities, which
can prevent some numerical methods from working, thus
can require some special handling. Many numerical methods
assume some form of continuity of the functions,
often including that of derivatives up to some order.
Handling the Riemann problem may require methods
involving more computation, which may be mitigated
by using approximations that handle the problem
reasonably.

For example, using the finite volume method to carry out
fluid dynamic calculations that include shock
can present the problem.

(*mathematics,computation*)
http://en.wikipedia.org/wiki/Riemann_problem

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