Abstract
We establish that the approximate solution of the mixed finite element method for the primary function is superconvergent to its $$L_2$$ local projection on unstructured meshes. To the best of our knowledge, all of the superconvergent results concerning mixed method need some conditions such as requiring the underlying meshes to be structured or using higher-order approximation spaces. Our results are valid on shape regular meshes, and any order of approximation spaces can be used. As an elementary consequence, we provide a proof that solutions of least-squares (LS) finite element method are higher-order perturbations of the solutions of the mixed and standard Galerkin methods. Also, we provide an $$L_2$$ norm error estimate for LS finite element solution on graded meshes.
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.
