Journal of Computational Physics
A discontinuous hp finite element method for diffusion problems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Mixed Finite Element Methods on Nonmatching Multiblock Grids
SIAM Journal on Numerical Analysis
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems
SIAM Journal on Numerical Analysis
A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Symmetric and Nonsymmetric Discontinuous Galerkin Methods for Reactive Transport in Porous Media
SIAM Journal on Numerical Analysis
Discontinuous Galerkin Methods for a Model of Population Dynamics with Unbounded Mortality
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
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We investigate DG-DG domain decomposition coupling using mortar finite elements to approximate the solution to general second-order partial differential equations. We weakly impose an inflow boundary condition on the inflow part of the interface and the Dirichlet boundary condition on the elliptic part of the interface via Lagrange multipliers. We obtain the matching condition by imposing the continuity of the total flux through the interface and the continuity of the solution on the elliptic parts of the interface. The diffusion coefficient is allowed to be degenerate and the mortar interface couples efficiently the multiphysics problems. The (discrete) problem is solvable in each subdomain in terms of Lagrange multipliers and the resulting algorithm is easily parallelizable. 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 then established. A non-overlapping parallelizable domain decomposition algorithm (Arbogast et al., 2007) reduces the coupled system to an interface mortar problem. The properties of the interface operator are discussed.