An adaptive finite element reconstruction of distributed fluxes

作者：Li, Jingzhi^*; Xie, Jianli; Zou, Jun

来源：Inverse Problems, 2011, 27(7): 075009.

DOI：10.1088/0266-5611/27/7/075009

• POSTERIORI ERROR ESTIMATION
• AUGMENTED LAGRANGIAN METHOD
• IDENTIFICATION
• PARAMETERS

Based on a posteriori error estimates, we propose an adaptive finite element method for a distributed flux reconstruction in a diffusion system, recovering the unknown distributed flux on some inaccessible boundary using partial measurement data on part of the accessible boundary. A posteriori error estimates are first derived, and then the efficiency of the error estimator is addressed by showing that it provides upper and lower bounds on the discretization errors of the quantities of interest. Numerical experiments are presented to show the applicability and efficiency of the proposed adaptive method based on the derived error estimator, which provides a robust guidance for the adaptive refining of meshes to locate the singularities of the fluxes.

• 出版日期2011-7
• 单位上海交通大学; 香港中文大学; 中国科学院深圳先进技术研究院