论文标题
DIV-CURL问题的数值解决方案有限元外孔
Numerical solution of the div-curl problem by finite element exterior calculus
论文作者
论文摘要
我们对在r 3或r 2的一般域中具有规定的差异和卷曲的向量场的数值重建感兴趣，不一定是可缩度的。为此，我们介绍了有限元外观微积分的一些基本概念，并严重依赖P. Leopardi和A. Stern的最新结果。本文的目的是利用通常的矢量演算与外部演算之间的联系，并显示外观演算框架的兴趣，而没有太多的对主题的知识。我们首先描述用于合同域的方法及其使用Fenics库的实现（请参阅FenicsProject.org）。然后，我们解决了与非合同域和一般边界条件遇到的问题，并解释了如何适应处理这些情况的方法。最后，我们在维度2和3中给出了使用此方法获得的一些数值结果。
We are interested in the numerical reconstruction of a vector field with prescribed divergence and curl in a general domain of R 3 or R 2 , not necessarily contractible. To this aim, we introduce some basic concepts of finite element exterieur calculus and rely heavily on recent results of P. Leopardi and A. Stern. The goal of the paper is to take advantage of the links between usual vector calculus and exterior calculus and show the interest of the exterior calculus framework, without too much prior knowledge of the subject. We start by describing the method used for contractible domains and its implementation using the FEniCS library (see fenicsproject.org). We then address the problems encountered with non contractible domains and general boundary conditions and explain how to adapt the method to handle these cases. Finally we give some numerical results obtained with this method, in dimension 2 and 3.
