Solution of Maxwell equation in axisymmetric geometry by Fourier series decompostion and by use of H (rot) conforming finite element
Solution of Maxwell equation in axisymmetric geometry by Fourier series decompostion and by use of H (rot) conforming finite element
复制标题
轴对称几何中麦克斯韦方程的傅立叶级数分解和使用 H (rot) 符合有限元的求解
作者：
P. Lacoste
摘要本文研究轴对称几何中时谐麦克斯韦方程的数学和数值解法。利用傅立叶分解，我们定义了加权Sobolev空间的解决方案，我们证明了预期的正则性结果。本文的一个实际贡献是构造了一类与H（rot）空间相一致的有限元，该有限元具有加权测度rdrdz。它是Raviart-Thomas-Nédélec [11]-[15]中著名的Carnival混合有限元的推广。这些单元是由经典的拉格朗日元和混合有限元构造的，因此不需要特殊的逼近函数。最后，根据Mercier和Raugel [10]的工作，我们对最简单的建议元素进行插值误差估计。
Summary. This study deals with the mathematical and numerical solution of time-harmonic Maxwell equation in axisymmetric geometry. Using Fourier decomposition, we define weighted Sobolev spaces of solution and we prove expected regularity results. A practical contribution of this paper is the construction of a class of finite element conforming with the H (rot) space equipped with the weighted measure rdrdz. It appears as an extension of the well-known cartesian mixed finite element of Raviart-Thomas-Nédélec [11]–[15]. These elements are built from classical lagrangian and mixed finite element, therefore no special approximations functions are needed. Finally, following works of Mercier and Raugel [10], we perform an interpolation error estimate for the simplest proposed element.