SIAM Journal on Scientific Computing, Volume 42, Issue 2, Page A1147-A1173, January 2020.
We present algebraic multigrid (AMG) methods for the efficient solution of the linear system of equations stemming from high-order discontinuous Galerkin (DG) discretizations of second-order elliptic problems. For DG methods, standard multigrid approaches cannot be employed because of redundancy of the degrees of freedom associated to the same grid point. We present new aggregation procedures and test them in extensive two-dimensional numerical experiments to demonstrate that the proposed AMG method is uniformly convergent with respect to all of the discretization parameters, namely the mesh-size and the polynomial approximation degree.

中文翻译：

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高阶节点间断Galerkin方法的代数多重网格方案

SIAM科学计算杂志，第42卷，第2期，第A1147-A1173页，2020年1月。
我们提出了代数多重网格（AMG）方法，用于有效解线性方程组的高阶不连续Galerkin（DG）离散化二阶椭圆问题。对于DG方法，由于与同一网格点关联的自由度的冗余，因此无法采用标准的多网格方法。我们提出了新的聚合程序，并在广泛的二维数值实验中对其进行了测试，以证明所提出的AMG方法相对于所有离散化参数（即网格大小和多项式逼近度）是均匀收敛的。