Abstract
A novel technique is proposed for analyzing the convergence of a projection difference scheme as applied to the initial value problem for a quasilinear parabolic operator-differential equation with initial data u0 ∈ H. The technique is based on the smoothing property of solutions to the differential problem for t > 0. Under certain conditions on the nonlinear term, a new estimate of order \(O(\sqrt \tau + h)\) for the convergence rate in a weighted energy norm is obtained without using a priori assumptions on the additional smoothness of weak solutions.
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: Computational Mathematics and Mathematical Physics
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.
