论文标题
二阶有限元法，巨大的质量大量用于四面体上的麦克斯韦方程
A second order finite element method with mass lumping for Maxwell's equations on tetrahedra
论文作者
论文摘要
我们考虑了时域中麦克斯韦方程的数值近似，二阶$ h（curl）$符合有限元近似。为了使有效地应用显式时间步进方案，我们利用了由数值集成与Elmkies和Joly引入的有限元空间结合使用的质量倾斜策略。我们证明，如果真正的解决方案不含分歧，则此方法是准确的，但是在一般情况下，准确度的顺序降低为一种。然后，我们建议对有限元空间进行修改，该空间在一般情况下产生二阶准确度。
We consider the numerical approximation of Maxwell's equations in time domain by a second order $H(curl)$ conforming finite element approximation. In order to enable the efficient application of explicit time stepping schemes, we utilize a mass-lumping strategy resulting from numerical integration in conjunction with the finite element spaces introduced by Elmkies and Joly. We prove that this method is second order accurate if the true solution is divergence free, but the order of accuracy reduces to one in the general case. We then propose a modification of the finite element space, which yields second order accuracy in the general case.
