A locally conservative, hybrid spectral difference method (HSD) is presented and analyzed for the Poisson equation. The HSD is composed of two types of finite difference approximations; the cell finite difference and the interface finite difference. Embedded static condensation on cell interior unknowns considerably reduces the global couplings, resulting in the system of equations in the cell interface unknowns only. A complete ellipticity analysis is provided. The optimal order of convergence in the semi-discrete energy norms is proved. Several numerical results are given to show the performance of the method, which confirm our theoretical findings.
Bibliographical noteFunding Information:
Y. Jeon was supported by National Research Foundation of Korea (NRF-2015R1D1A1A09057935). E.-J. Park was supported by National Research Foundation of Korea (NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358).
© 2017 by De Gruyter.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics