Abstract
Discontinuous Galerkin (DG) and mixed finite element (MFE) methods are two popular methods that possess local mass conservation. In this paper we investigate DG-DG and DG-MFE domain decomposition couplings using mortar finite elements to impose weak continuity of fluxes and pressures on the interface. The subdomain grids need not match, and the mortar grid may be much coarser, giving a two-scale method. Convergence results in terms of the fine subdomain scale h and the coarse mortar scale H are established for both types of couplings. In addition, a nonoverlapping parallel domain decomposition algorithm is developed, which reduces the coupled system to an interface mortar problem. The properties of the interface operator are analyzed.
Original language | English (US) |
---|---|
Pages (from-to) | 949-979 |
Number of pages | 31 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 46 |
Issue number | 2 |
DOIs | |
State | Published - 2008 |
Externally published | Yes |
Keywords
- Discontinuous Galerkin
- Flow in porous media
- Interface problem
- Mixed finite element
- Mortar finite element
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics