Preprint A669/2010
FETI-DP method for DG discretization of elliptic problems with discontinuous coefficients

Marcus Sarkis | Dryja, Maksymilian

**Keywords: **
interior penalty discretization | discontinuous Galerkin |
elliptic problems with discontinuous coefficients. finite element method |
FETI-DP algorithms | preconditioners

In this paper a discontinuous Galerkin (DG) discretization
of an elliptic two-dimensional problem with discontinuous
coefficients is considered. The problem is posed on a polygonal
region $\Omega$ which is a union of disjoint polygonals $\Omega_i$
of diameter $O(H_i)$ and forms a geometrically conforming
partition of $\Omega$. The discontinuities of the coefficients
are assumed to occur only across $\partial \Omega_i$. Inside
of each substructure $\Omega_i$, a conforming finite element space
on a quasiuniform triangulation with triangular elements and mesh
size $O(h_i)$ is introduced. To handle the nonmatching meshes
across $\partial \Omega_i$,
a discontinuous Galerkin discretization is considered. For solving
the resulting discrete problem, a FETI-DP method is designed
and analyzed. It is established that the condition number of the method
is estimated by
$C(1 + \max_i \log H_i/h_i)^2$ with a constant $C$ independent of
$h_i$, $H_i$ and the jumps of the coefficients. The method is well suited for
parallel computations and it can be straightforwardly extended to
three-dimensional problems.