A nonconforming finite element method for a two-dimensional curl–curl and grad-div problem
A nonconforming finite element method for a two-dimensional curl–curl and grad-div problem
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DOI：
10.1007/s00211-008-0149-7
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发表时间：
2008-05
影响因子：
2.1
通讯作者：
S. C. Brenner;Jintao Cui;Fengyan Li;L. Sung
中科院分区：
文献类型：
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作者：
S. C. Brenner;Jintao Cui;Fengyan Li;L. Sung
本文研究了二维旋度-旋度和梯度-div问题的数值方法。它基于使用弱连续 P1 向量场的离散化，并包括两个涉及向量场跨元素边界跳跃的一致性项。能量范数和 L2 范数的最佳收敛速率（最多为任意正数）是在分级网格上建立的。理论结果得到数值实验的证实。
A numerical method for a two-dimensional curl–curl and grad-div problem is studied in this paper. It is based on a discretization using weakly continuousP1vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries. Optimal convergence rates (up to an arbitrary positive) in both the energy norm and theL2norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.