论文标题
与线性双曲线方程的中央通量不连续的Galerkin方法的次优融合，具有均匀度多项式近似值
Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations
论文作者
论文摘要
在本文中，我们从理论和数字上验证了在非均匀网格上的线性双曲线方程中具有中央通量的不连续的Galerkin（DG）方法，当在$ L^2 $ norm中测量均匀的多项近似值时，在$ l^2 $ norm中测量时具有次优的收敛属性。在均匀的网格上，为一个和多维中的任意单元格提供了最佳误差估计，从而改善了先前的结果。发现理论发现与数值结果一致。
In this paper, we theoretically and numerically verify that the discontinuous Galerkin (DG) methods with central fluxes for linear hyperbolic equations on non-uniform meshes have sub-optimal convergence properties when measured in the $L^2$-norm for even degree polynomial approximations. On uniform meshes, the optimal error estimates are provided for arbitrary number of cells in one and multi-dimensions, improving previous results. The theoretical findings are found to be sharp and consistent with numerical results.
