论文标题
与对称溶液的部分微分方程对称的两尺度有限元离散化
Symmetrized two-scale finite element discretizations for partial differential equations with symmetric solutions
论文作者
论文摘要
在本文中，为具有对称溶液的一类偏微分方程提出了对称的两尺度有限元方法。使用此方法，将细量量元件网格上的有限元近似降低到有限元近似值，并在大量粗网格和单变量的细网格上近似。理论和数字包括电子结构计算表明，所产生的近似仍然保持渐近的最佳精度。因此，对称的两尺度有限元方法大大降低了计算成本。
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to the finite element approximations on a much coarse grid and a univariant fine grid. It is shown by both theory and numerics including electronic structure calculations that the resulting approximation still maintains an asymptotically optimal accuracy. Consequently the symmetrized two-scale finite element method reduces computational cost significantly.
