Interior penalty method for the indefinite time-harmonic Maxwell equations
Interior penalty method for the indefinite time-harmonic Maxwell equations
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DOI：
10.1007/s00211-005-0604-7
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发表时间：
2005-05
影响因子：
2.1
通讯作者：
P. Houston;I. Perugia;A. Schneebeli;D. Schötzau
中科院分区：
文献类型：
--
作者：
P. Houston;I. Perugia;A. Schneebeli;D. Schötzau
本文介绍并分析了高频区无限时谐麦克斯韦方程数值离散的内罚不连续Galerkin方法。基于适当的对偶论证，我们得到了能量范数和L2范数的先验误差界。特别地，关于解析解的网格尺寸、多项式次数ℓ和正则性指数，证明了能量范数的误差收敛于最优阶(Hmin{S，ℓ})。在附加的正则性假设下，证明了L2误差收敛于最优阶(hℓ+1)。理论结果在一系列数值实验中得到了证实。
In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of theindefinitetime-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and theL2-norm. In particular, the error in the energy norm is shown to converge with the optimal order (hmin{s,ℓ}) with respect to the mesh sizeh, the polynomial degree ℓ, and the regularity exponentsof the analytical solution. Under additional regularity assumptions, theL2-error is shown to converge with the optimal order (hℓ+1). The theoretical results are confirmed in a series of numerical experiments.