New Mixed Elements for Maxwell Equations
New Mixed Elements for Maxwell Equations
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DOI：
10.1137/18m1168054
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发表时间：
2019-02
期刊：
影响因子：
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通讯作者：
Huoyuan Duan;Zhijie Du;W. Liu;Shangyou Zhang
中科院分区：
文献类型：
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作者：
Huoyuan Duan;Zhijie Du;W. Liu;Shangyou Zhang
提出了一种新的基于电场和拉格朗日乘子的求解麦克斯韦方程组的inf-super稳定混合元。在二维和三维空间中的单形上的任意阶的节点连续的拉格朗日元素可用于电场。乘子总是用不连续的分段常数元相容地逼近。一般理论的稳定性和误差估计的发展，当应用到本征值问题，我们表明，建议的混合元素提供频谱正确的，spurious-free近似。本质上最优的误差界（只有一个任意小的常数）的特征值和奇异和光滑的解决方案。数值实验验证了理论结果。
New inf-sup stable mixed elements are proposed and analyzed for solving the Maxwell equations in terms of electric field and Lagrange multiplier. Nodal-continuous Lagrange elements of any order on simplexes in two- and three-dimensional spaces can be used for the electric field. The multiplier is compatibly approximated always by the discontinuous piecewise constant elements. A general theory of stability and error estimates is developed; when applied to the eigenvalue problem, we show that the proposed mixed elements provide spectral-correct, spurious-free approximations. Essentially optimal error bounds (only up to an arbitrarily small constant) are obtained for eigenvalues and for both singular and smooth solutions. Numerical experiments are performed to illustrate the theoretical results.