Abstract
We identify and study an LDG-hybridizable Galerkin method, which is not an LDG method, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuous Galerkin methods using polynomials of degree k ≥ 0 for both the potential as well as the flux, the order of convergence in L 2 of both unknowns is k + 1. Moreover, both the approximate potential as well as its numerical trace superconverge in L 2 -like norms, to suitably chosen projections of the potential, with order k + 2. This allows the application of element-by-element postprocessing of the approximate solution which provides an approximation of the potential converging with order k+2 in L 2 . The method can be thought to be in between the hybridized version of the Raviart-Thomas and that of the Brezzi-Douglas-Marini mixed methods.
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.
