论文标题
时间谐波麦克斯韦方程的不连续的最小二乘有限元法
A discontinuous least squares finite element method for time-harmonic Maxwell equations
论文作者
论文摘要
我们提出和分析了一种不连续的最小二乘有限元方法，用于解决无限期的谐音麦克斯韦方程。该方案基于$ l^2 $规范最小二乘正方形的功能，其连续性在整个内部面上都较弱。我们最大程度地减少了分段多项式空间以寻求数值解决方案的功能。该方法显示稳定，而对网格大小没有任何限制。我们证明了能源规范和$ l^2 $规范下的收敛订单。提出了两个维度和三个维度的数值结果，以验证误差估计。
We propose and analyze a discontinuous least squares finite element method for solving the indefinite time-harmonic Maxwell equations. The scheme is based on the $L^2$ norm least squares functional with the weak imposition of the continuity across the interior faces. We minimize the functional over the piecewise polynomial spaces to seek numerical solutions. The method is shown to be stable without any constraint on the mesh size. We prove the convergence orders under both the energy norm and the $L^2$ norm. Numerical results in two and three dimensions are presented to verify the error estimates.
