Abstract
The convergence of a class of continuous Galerkin methods for the nonlinear (cubic) Schrödinger equation is analyzed in this paper. These methods allow variable temporal stepsizes as well as changing of the spatial grid from one time level to the next. We show the existence of the resulting approximations and prove optimal order error estimates in $L^\infty (L^2 ) $ and in $L^\infty (H^1 ) .$ These estimates are valid under weak restrictions on the space-time mesh. These restrictions are milder if the elliptic projection is used at every time step instead of the L2 projection. We also give superconvergence results at the temporal nodes tn .
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 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.
