We propose and analyze a domain decomposition method on non-matching grids
for partial differential equations with non-negative
characteristic form. No weak or strong continuity of the finite
element functions, their normal derivatives, or linear
combinations of the two is imposed across the boundaries of the subdomains.
Instead, we employ suitable bilinear forms defined on the common
interfaces, typical of discontinuous Galerkin
We prove an error bound which is optimal with respect to the mesh–size and
suboptimal with respect to the polynomial degree.
Our analysis is valid for arbitrary shape–regular meshes and arbitrary
partitions into subdomains.
Our method can be applied to advective, diffusive, and mixed–type equations,
and is well-suited for problems coupling hyperbolic and elliptic equations.
We present some two-dimensional
numerical results that support our analysis for the case of
linear finite elements.