AN Hdiv-BASED MIXED QUASI-REVERSIBILITY METHOD FOR SOLVING ELLIPTIC CAUCHY PROBLEMS
AN Hdiv-BASED MIXED QUASI-REVERSIBILITY METHOD FOR SOLVING ELLIPTIC CAUCHY PROBLEMS
复制标题
一种基于Hdiv的混合准可逆求解椭圆柯西问题的方法
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Hannukainen
中科院分区：
文献类型：
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作者：
J. Dardé;A. Hannukainen
抽象的。本文研究了有界区域上二阶椭圆算子的柯西问题。引入了一种新的拟可逆方法，以正则化的方式逼近不适定柯西问题的解。该方法基于H × Hdiv上的一个适定混合变分问题，其相应的解对单调收敛于Cauchy问题的解和相应的通量（如果它们存在的话）.证明了正则化问题可以用拉格朗日和Raviart-Thomas有限元离散。所得到的数值算法的功能进行了测试，通过三维数值模拟数据的基础上的实验。柯西问题和一个相关的逆障碍问题的拉普拉斯算子。
Abstract. This work considers the Cauchy problem for a second order elliptic operator in a bounded domain. A new quasi-reversibility approach is introduced for approximating the solution of the illposed Cauchy problem in a regularized manner. The method is based on a well-posed mixed variational problem on H × Hdiv, with the corresponding solution pair converging monotonically to the solution of the Cauchy problem and the associated flux, if they exist. It is demonstrated that the regularized problem can be discretized using Lagrange and Raviart–Thomas finite elements. The functionality of the resulting numerical algorithm is tested via three-dimensional numerical experiments based on simulated data. Both the Cauchy problem and a related inverse obstacle problem for the Laplacian are considered.
凸源支撑及其在电阻抗层析成像中的应用
DOI：
10.1137/080715640
发表时间：
2008
期刊：
SIAM J. Imaging Sci.
影响因子：
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作者：
M. Hanke;N. Hyvönen;S. Reusswig
通讯作者：
S. Reusswig