  We present numerical techniques based on generalized functions adapted to
nonlinear calculations. They concern main numerical engineering problems ruled
by-or issued from-nonlinear equations of continuum mechanics. The aim of this
text is to invite the readers in applying these techniques in their own work
without significant prerequisites by presenting their use on a sample of
elementary applications from engineering. Pure mathematicians can read it
easily since the numerical techniques are fully recalled in a very simple way
and these applied mathematics are indeed based on nonlinear pure mathematics,
namely on the use of generalized functions adapted to nonlinear calculations.
The "nonlinear generalized functions" permit to compute explicit solutions of
simple problems, called Riemann problems, in cases in which this is not
possible using classical generalized functions (such as the distributions).
These explicit solutions are the elementary building blocks of efficient
numerical schemes needed by engineers.This text was prepared for an engineering
meeting. For mathematicians it is an illustration of general introductions to
these "nonlinear generalized functions". For physicists it complements,
concerning continuum mechanics, the use of the nonlinear generalized functions
in general relativity.
