Hybridized Discontinuous Galerkin Method with Lifting Operator

UTMS 2009–21 Hajime Fujita, Mikio Furuta and Takahiko Yoshida: Torus fibrations and lo-calization of index II-Local index for acyclic compatible system-. Cauchy data for general second order elliptic operators in two dimensions. 2009–23 Yukihiro Seki: On exact dead-core rates for a semilinear heat equation with strong absorption. 2009–24 Yohsuke Takaoka: On existence of models for the logical system MPCL. 2009–25 Takefumi Igarashi and Noriaki Umeda: Existence of global solutions in time for Reaction-Diffusion systems with inhomogeneous terms in cones. 2010–1 Norikazu Saito: Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis. 2010–2 Mourad Bellassoued and Masahiro Yamamoto: Carleman estimate with second large parameter for a second order hyperbolic operators in a Riemannian manifold. 2010–3 Kazufumi Ito, Bangti Jin and Tomoya Takeuchi: A regularization parameter for nonsmooth Tikhonov regularization. 2010–4 Tomohiko Ishida: Second cohomology classes of the group of C 1-flat diffeomor-phisms of the line. 2010–6 Issei Oikawa: Hybridized discontinuous Galerkin method with lifting operator. Formerly there were two departments of mathematics in the University of Tokyo: one in the Faculty of Science and the other in the College of Arts and Sciences. All faculty members of these two departments have moved to the new graduate school, as well as several members of the Department of Pure and Applied Sciences in the College of Arts and Sciences. In January, 1993, the preprint series of the former two departments of mathematics were unified as the Preprint Series of the Graduate School of Mathematical Sciences, The University of Tokyo. For the information about the preprint series, please write to the preprint series office. Abstract In this paper, we propose a new hybridized discontinuous Galerkin method for the Poisson equation with homogeneous Dirichlet boundary condition. Our method has the advantage that the stability is better than the previous hybridized method. We derive L 2 and H 1 error estimates of optimal order. Some numerical results are presented to verify our analysis.