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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method
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Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method

机译:使用割元的虚拟域有限元方法:I.稳定的拉格朗日乘数法

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摘要

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 exten-sion) of the cut elements in the mesh defining the primal variable. Inf-sup stability is obtained by penal-izing 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.
机译: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为止。解决方案本身也由域外部的节点定义,但是弱有限元形式仅涉及位于域内部的那些部分。乘法器被定义为在定义原始变量的网格中,剪切元素在整个(包括扩展)上都是元素常量。通过惩罚乘数在元件面上的跳跃,可以获得Inf-sup稳定性。我们考虑具有可能弯曲边界的多边形域的情况。该方法具有最佳的收敛特性。

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