Abstract
In this paper, the superconvergence error analysis of an energy-conserving Galerkin fully discrete scheme is proposed and investigated for the two-dimensional sine-Gordon equation. The unique solvability of the numerical scheme as well as the energy conservation are studied firstly. Then, based on the special property of the bilinear element on the rectangular mesh and the superclose estimate between interpolation and Ritz projection of the exact solution in H 1 -norm, the global superconvergence result in H 1 -norm is obtained in terms of a post-processing technique. Finally, numerical results are provided to confirm the energy conservation and superconvergence properties.
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 call
