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We study the convergence of iterative linear solvers for discontinuousGalerkin discretizations of systems of hyperbolic conservation laws withpolygonal mesh elements compared with that of traditional triangular elements.We solve the semi-discrete system of equations by means of an implicit timediscretization method, using iterative solvers such as the block Jacobi methodand GMRES. We perform a von Neumann analysis to analytically study theconvergence of the block Jacobi method for the two-dimensional advectionequation on four classes of regular meshes: hexagonal, square,equilateral-triangular, and right-triangular. We find that hexagonal and squaremeshes give rise to smaller eigenvalues, and thus result in faster convergenceof Jacobi's method. We perform numerical experiments with variable velocityfields, irregular, unstructured meshes, and the Euler equations of gas dynamicsto confirm and extend these results. We additionally study the effect ofpolygonal meshes on the performance of block ILU(0) and Jacobi preconditionersfor the GMRES method.

On the convergence of iterative solvers for polygonal discontinuous Galerkin discretizations