Abstract
We derive a rigorous {ital a} {ital posteriori} bound on the error in energy eigenvalues obtained using {ital C}{sup 1} finite elements, as well as several {ital a} {ital posteriori} error estimates, and test them numerically with potentials of analytically-known eigenspectrum. We also obtain numerical solutions, with error bounds and estimates, for the octic oscillator potential, illustrating the ability of the finite-element method to resolve-nearly degenerate states with extremely narrow splitting. The incorporation of adaptive refinement is shown to reduce the number of degrees of freedom needed to achieve a given level of accuracy.
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.
