Sub-Optimal Convergence of Discontinuous Galerkin Methods with Central Fluxes for Linear Hyperbolic Equations with Even Degree Polynomial Approximations (Journal of Computational Mathematics, 2021)
In this paper, we theoretically and numerically verify that the discontinuous Galerkin(DG) methods with central fluxes for linear hyperbolic equations on non-uniform mesheshave sub-optimal convergence properties when measured in the $L^2$-norm for even degreepolynomial approximations. On uniform meshes, the optimal error estimates are providedfor arbitrary number of cells in one and multi-dimensions, improving previous results. Thetheoretical findings are found to be sharp and consistent with numerical results.