Abstract
We present both time and space-time explicit approximation schemes for a system of first-order nonlinear transport PDEs used as a model in chemical engineering. For the time discretization, using a splitting, we introduce an intermediate spatial regularization step to obtain some bounded variation (BV) estimates for the approximate solutions (with BV initial data), and we get an $O(\Delta t^{1/2})$ $L^1$ convergence rate. With respect to the fully discrete finite volume scheme, we show that it is possible to get such estimates without any regularization step because of the dissipative effect of the upwind scheme used to treat the transport part of the equations. This scheme is convergent.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
