Block Jacobi for Discontinuous Galerkin Discretizations: No Ordinary Schwarz Methods

For classical discretizations of elliptic partial differential equations, like conforming finite elements or finite differences, block Jacobi methods are equivalent to classical Schwarz methods with Dirichlet transmission conditions. This is however not necessarily the case for discontinuous Galerkin methods (DG). We will show for the model problem \(-\varDelta u = f\) and various DG discretizations that a block Jacobi method applied to the discretized problem can be interpreted as a Schwarz method with different transmission conditions.