A New Moving Mesh Algorithm for the Finite Element Solution of Variational Problems
A New Moving Mesh Algorithm for the Finite Element Solution of Variational Problems
复制标题
变分问题有限元求解的一种新的移动网格算法
DOI：
10.1137/s0036142996313932
复制
发表时间：
1998
影响因子：
2.9
通讯作者：
F. Hülsemann
中科院分区：
文献类型：
--
作者：
Y. Tourigny;F. Hülsemann
给出了无限维空间中变分问题有限元解的一种新的迭代网格优化算法的描述和应用。最优准则是网格应该是这样的，即在有限元近似下计算的变分“能量泛函”是最小化的。这种准则在有限元文献中有较长的历史。本文提出的方法的主要优点是，网格的每个节点和离散近似的相应节点值都是通过逐次求解自由度很少的局部极小化问题来更新的。结果表明，该方法对能量泛函的简化是单调的，不需要在中间阶段求解整体离散问题。讨论了偏微分方程解的应用。将该算法与Bank著名的PLTMG椭圆求解器相结合，得到了二维的数值结果。
The paper is devoted to the description and application of a new iterative mesh optimization algorithm for the finite element solution of variational problems set in infinite-dimensional spaces. The optimality criterion is that the mesh should be such that the variational "energy functional," evaluated at the finite element approximation, be minimized. Such a criterion has a relatively long history in the finite element literature. The chief merit of the procedure presented in this paper is that each node of the mesh, and the corresponding nodal value of the discrete approximation, are updated by solving sequentially local minimization problems with very few degrees of freedom. It is shown that this procedure reduces the energy functional monotonically, without the need to solve the global discrete problem at intermediate stages. Applications to partial differential equations are considered. Numerical results in two dimensions are obtained by incorporating the algorithm into Bank's well-known PLTMG elliptic solver.