Agglomeration-based physical frame dG discretizations: An attempt to be mesh free
Agglomeration-based physical frame dG discretizations: An attempt to be mesh free
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DOI：
10.1142/s0218202514400028
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发表时间：
2014-07-01
影响因子：
3.5
通讯作者：
Colombo, Alessandro
中科院分区：
文献类型：
--
作者：
Bassi, Francesco;Botti, Lorenzo;Colombo, Alessandro
在这项工作中，我们认为基于凝聚的物理框架间断Galerkin(DG)离散化是提高高阶有限元方法灵活性的一种有效方法。无网格概念在以下(广义)意义上被追求：计算域仍然使用网格进行离散，但计算网格不应成为有限元离散的约束。特别是离散空间的选择，其收敛性质，甚至由DG离散化产生的整体方程组的求解的复杂性不应受到网格选择的影响。物理帧DG离散化允许获得与网格无关的h-收敛速度。由于网格的凝聚，可以在任意粗糙的网格上执行高精度的离散，而不需要求助于区域边界的非常高阶近似。基于凝聚的h-多重网格技术是获得快速、独立于网格的解算器的明显选择。这些特点(对任何无网格离散化都很有吸引力)在实践中通过数值试验得到了验证。
In this work we consider agglomeration-based physical frame discontinuous Galerkin (dG) discretization as an effective way to increase the flexibility of high-order finite element methods. The mesh free concept is pursued in the following (broad) sense: the computational domain is still discretized using a mesh but the computational grid should not be a constraint for the finite element discretization. In particular the discrete space choice, its convergence properties, and even the complexity of solving the global system of equations resulting from the dG discretization should not be influenced by the grid choice. Physical frame dG discretization allows to obtain mesh-independent h-convergence rates. Thanks to mesh agglomeration, high-order accurate discretizations can be performed on arbitrarily coarse grids, without resorting to very high-order approximations of domain boundaries. Agglomeration-based h-multigrid techniques are the obvious choice to obtain fast and grid-independent solvers. These features (attractive for any mesh free discretization) are demonstrated in practice with numerical test cases.