Abstract
We present a dual finite element method for a singularly perturbed reaction-diffusion problem. It can be considered a reduced version of the mixed finite element method for approximate solutions. The new method only approximates the dual variables without approximating the primary variable. An approximation for the primary variable is recovered through a simple local $L_2$ projection. Optimal error estimates for the primary and flux variables are obtained. Our method provides a competitive alternative to other existing numerical methods. For example, our approximate solution for the primary variable does not show a significant numerical oscillation, which is observed in the standard Galerkin methods, and we present a confirming numerical example.
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.
