Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method
Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method
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DOI：
10.1016/j.cma.2010.05.011
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发表时间：
2010-01-01
影响因子：
7.2
通讯作者：
Hansbo, Peter
中科院分区：
文献类型：
--
作者：
Burman, Erik;Hansbo, Peter
我们提出了一种虚拟域方法，其中网格被边界切割。原始解仅计算到边界；解本身也由域外的节点定义，但弱有限元形式仅涉及位于域内的单元部分。乘数被定义为定义原始变量的网格中切割元素的整体（包括延伸）上的元素常数。 Inf-sup 稳定性是通过惩罚单元面上乘数的跳跃来获得的。我们考虑具有可能弯曲边界的多边形域的情况。该方法具有最优收敛特性。 (C) 2010 Elsevier B.V. 保留所有权利。
We propose a fictitious domain method where the mesh is cut by the boundary. The primal solution is computed only up to the boundary; the solution itself is defined also by nodes outside the domain, but the weak finite element form only involves those parts of the elements that are located inside the domain. The multipliers are defined as being element-wise constant on the whole (including the extension) of the cut elements in the mesh defining the primal variable. Inf-sup stability is obtained by penalizing the jump of the multiplier over element faces. We consider the case of a polygonal domain with possibly curved boundaries. The method has optimal convergence properties. (C) 2010 Elsevier B.V. All rights reserved.