  The minimization of operation costs for natural gas transport networks is
studied. Based on a recently developed model hierarchy ranging from detailed
models of instationary partial differential equations with temperature
dependence to highly simplified algebraic equations, modeling and
discretization error estimates are presented to control the overall error in an
optimization method for stationary and isothermal gas flows. The error control
is realized by switching to more detailed models or finer discretizations if
necessary to guarantee that a prescribed model and discretization error
tolerance is satisfied in the end. We prove convergence of the adaptively
controlled optimization method and illustrate the new approach with numerical
examples.
