Regularity and approximation of systems arising in electromagnetic interrogation of dielectric materials
Regularity and approximation of systems arising in electromagnetic interrogation of dielectric materials
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DOI：
10.1080/01630569908816914
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发表时间：
1999
影响因子：
1.2
通讯作者：
H. Banks;J. Zou
中科院分区：
文献类型：
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作者：
H. Banks;J. Zou
在本文中，我们关注的是一个数学模型，它描述了电介质材料的电磁询问。我们解决了系统的适定性和正则性的解决方案。然后，我们提出了一个半离散有限元逼近的系统，并证明了弱收敛在非常温和的正则性假设下的原系统的解决方案。我们还建立了解决方案具有较高的规律性，即使输入源可能是一个窗口的分布型信号。然后利用这一规律性证明了有限元解的强收敛性。
In this paper we are concerned with a mathematical model which describes the electromagnetic interrogation of dielectric materials. We address the well-posedness of the system and regularity of solutions. Then we propose a semi-discrete finite element scheme for approximating the system and prove weak convergence under very mild regularity assumptions on the solutions of the original system. We also establish that the solution has higher regularity in time even though the input source may be a windowed signal of distributional type. This regularity is then utilized to show the strong convergence of the finite element solution.