Lecture by Prof. Youngmok Jeon on Numerical PDE
August 25th (Friday) at 11:00-12:00
National Institute of Informatics
Room 1212 (Lecture Room 1)
The Hybrid Difference Method
Professor Youngmok Jeon
Department of Mathematics, Ajou University, Korea
We introduce the hybrid difference method (HDM) for the elliptic andNavier-Stokes equations. The HDM is a finite difference version of the hybridized discontinuous Galerkin method. The HDM is comparable with the finite difference method (FDM). The main difference between the FDM and HDM is that the FD formula of a single type is deployed for all interior nodes in the FDM, while the cell finite difference and the interface difference are combined in the HDM.
The HDM is as easy to implement as the FDM, and it apparently seems to possess several advantages over the FDM. Those advantages are listed below.
- The method can be applied to nonuniform grids, retaining the optimal order of convergence. The FD formulas in a reference cell can be applied to cells of any dimension, multiplied by scaling factors.
- Problems on a complicated geometry can be treated reasonably well, and the boundary condition can be imposed exactly on the exact boundary.
- Stability problems when solving the Stokes/Navier-Stokes problem can be resolved without introducing a staggered grid or a stream-vorticity formulation.
- Numerical analysis is based on a discrete divergence theory on each cell.
- The static condensation property of the HDM is naturally embedded.
Ken Hayami (hayami(at)nii.ac.jp)