Abstract
The dual argument is well known for recoving the optimal L2-error of the finite element method in elliptic context. This argument, however, will lose efficacy in hyperbolic case. An expansion argument and an approximation argument are presented in this paper to recover the optimal L2-error of finite element methods for hyperbolic problems. In particular, a second order error estimate in L2-norm for the standard linear finite element method of hyperbolic problems is obtained if the exact solution is smooth and the finite element mesh is almost uniform, and some superconvergence estimates are also established for less smooth solution.
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.
