Abstract
We propose an error analysis for a shock capturing finite element method for the Burgers' equation using the duality theory due to Tadmor. The estimates use a one-sided Lipschitz stability (Lip+-stability) estimate on the discrete solution and are obtained in a weak norm, but thanks to a total variation a priori bound on the discrete solution and an interpolation inequality, error estimates in Lp-norms (1 ≤ p < ∞) are deduced. Both first-order artificial viscosity and a nonlinear shock capturing term that formally is of second order are considered. For the discretization in time we use the forward Euler method. In the numerical section we verify the convergence order of the nonlinear scheme using the forward Euler method and a second-order strong stability preserving Runge–Kutta method. We also study the Lip+-stability property numerically and give some examples of when it holds strictly and when it is violated.
Sign-in/Register to access full text options 
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 callMore From: Mathematical Models and Methods in Applied Sciences
Disclaimer: 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.
