Error analysis of a dynamic model adaptation procedure for nonlinear hyperbolic equations (Q900230)

The authors derive in this paper an error estimate for a simple algorithm of dynamic model adaptation applied to nonlinear hyperbolic equations. In order to theoretical a dynamic model adaptation method, they consider a simple case where the model error can be analyzed. The dynamical model adaption consists of detecting at each time step the rigion where a given fine model can be replaced by a corresponding coarse model without deteriorating the accuracy and to couple the two models, each being computed on its respective region. The adaptation method provides an intermediate adapted solution which results from the coupling of both models at each time step. Finally, the authors provide some numerical computations to illustrate the optimality of result.