数値解析セミナー

過去の記録 ~11/11次回の予定今後の予定 11/12~

開催情報 火曜日 16:30~18:00 数理科学研究科棟(駒場) 056号室
担当者 齊藤宣一
セミナーURL http://www.infsup.jp/utnas/

2019年08月19日(月)

13:00-17:00   数理科学研究科棟(駒場) 122号室
"Mini Workshop on Recent Developments in Discontinuous Galerkin Methods"として開催
Eric Chung 氏 (The Chinese University of Hong Kong) 13:00-14:00
Staggered hybridisation for discontinuous Galerkin methods (英語)
[ 講演概要 ]
In this talk, we present a new staggered hybridization technique for discontinuous Galerkin methods to discretize linear elastodynamic equations and nonlinear Stokes equations. The idea of hybridization is used extensively in many discontinuous Galerkin methods, but the idea of staggered hybridization is new. Our new approach offers several advantages, namely energy conservation, high-order optimal convergence, preservation of symmetry for the stress tensor, block diagonal mass matrices as well as low dispersion error. The key idea is to use two staggered hybrid variables to enforce the continuity of the velocity and the continuity of the normal component of the stress tensor on a staggered mesh. We prove the stability and the convergence of the proposed scheme in both the semi-discrete and the fully-discrete settings. Numerical results confirm the optimal rate of convergence and show that the method has a superconvergent property for dispersion.
Feifei Jing 氏 (Northwestern Polytechnical University) 14:30-15:30
DG and HDG methods for the variational inequality problems (英語)
[ 講演概要 ]
There exist many numerical methods for solving the fluid dynamics equations, the main difference between them lies in the partitions of geometric domain and the discrete forms of governing equations. Due to the discontinuous piecewise polynomial subspaces, DG and HDG methods can be easily implemented on highly unstructured meshes, e.g. general polygonal mesh, and volume integrals could be calculated on physical elements, without reference elements and mappings between physical and reference elements. In this talk, DG and HDG methods employed to a class of variational inequality problems arising in hydrodynamics are studied. Some theoretical results will be shown, as well as the implementations of these methods are also put into practice.
及川一誠 氏 (一橋大学) 16:00-16:30
A new HDG method using a hybridized flux (英語)
[ 講演概要 ]
We propose a new hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems. In our method, both the trace and flux of the exact solution are hybridized. The Lehrenfeld-Schöberl stabilization is implicitly included in the method, so that the orders of convergence in all variables are optimal without postprocessing and computation of any projection. Numerical results are present to show the validation of our method.
柏原崇人 氏 (東京大学) 16:30-17:00
Numerical approximation of the Stokes–Darcy problem using discontinuous linear elements (英語)
[ 講演概要 ]
We consider the Stokes–Darcy interface problem supplemented with the Beavers– Joseph–Saffman condition on the interface separating two domains. This condition allows for discontinuity in the tangential velocities and in the pressures along the interface. To effectively express it, we propose to use discontinuous linear finite elements to approximate all of the velocities/pressures in the Stokes/Darcy regions. The continuity of velocity in the normal direction is weakly enforced by adopting either the penalty method or Nitsche’s method. We present stability and error estimates for the proposed scheme, taking into account the situation where a curved interface is approximated by a polygonal curve or polyhedral surface.