论文标题
$ hp $ -robust Multigrid求解器在本地精制网格上，用于对称椭圆pdes的FEM离散
$hp$-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs
论文作者
论文摘要
在这项工作中，我们制定和分析了一种几何多移民方法，用于由对称二阶线性椭圆扩散问题的有限元离散化产生的离散系统的迭代解决方案。我们表明，迭代求解器相对于多项式学位$ p \ ge 1 $和（本地）网格尺寸$ h $签订了代数错误。我们进一步证明，求解器随附的内置代数误差估计器是$ hp $ - 完全等同于代数错误。概述了求解器在自适应有限元方法框架内使用准最佳计算成本的应用。数值实验证实了理论发现。
In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric second-order linear elliptic diffusion problems. We show that the iterative solver contracts the algebraic error robustly with respect to the polynomial degree $p \ge 1$ and the (local) mesh size $h$. We further prove that the built-in algebraic error estimator which comes with the solver is $hp$-robustly equivalent to the algebraic error. The application of the solver within the framework of adaptive finite element methods with quasi-optimal computational cost is outlined. Numerical experiments confirm the theoretical findings.
