Adjoint-based error estimation for the front-tracking method.

摘要

We show how to measure the error in a functional of the front-tracking approximations by using the adjoint method. This work is restricted to nonlinear scalar conservation laws containing only shock waves. We construct a piecewise linear approximation to the adjoint of the error equation for the piecewise constant front-tracking approximations. We show that under certain conditions, this can be used to bound the error. The construction of the adjoint is new and based on a scheme that is dual to the front-tracking scheme.