Adaptive error estimation of the Trefftz method for solving the Cauchy problem

C. T. Chen, K. H. Chen, J. F. Lee, J. T. Chen

研究成果: Conference contribution

摘要

In this paper, the Laplace problem with overspecified boundary conditions is investigated by using the Trefftz method. The main difficulty will appear an obvious divergent result when the boundary condition on an overspecified boundary contaminates artificial errors. The occurring mechanism of the unreasonable result originates from an ill-posed influence matrix. The accompanied ill-posed problem is remedied by using the Tikhonov regularization technique and the linear regularization method respectively, to reconstruct the influence matrix. The optimal parameters of the Tikhonov technique and linear regularization method are determined by adopting the adaptive error estimation technique. The numerical evidence of the Trefftz method is given to verify the accuracy of the solutions after comparison with the results of analytical solution and to demonstrate the validity and instructions of the proposed adaptive error estimation technique. The comparison of the Tikhonov regularization technique and the linear regularization method was also discussed in the example.

原文English
主出版物標題Boundary Elements and Other Mesh Reduction Methods XXIX
頁面43-56
頁數14
DOIs
出版狀態Published - 2007 十二月 1
事件29th International Conference on Boundary Elements and other Mesh Reduction Methods: Incorportaing A Seminar on Computational and Experimental Methods in Electrical Engineering and Electromagnetics, BEM/MRM 29 - The New Forest, United Kingdom
持續時間: 2007 六月 42007 六月 6

出版系列

名字WIT Transactions on Modelling and Simulation
44
ISSN(列印)1743-355X

Other

Other29th International Conference on Boundary Elements and other Mesh Reduction Methods: Incorportaing A Seminar on Computational and Experimental Methods in Electrical Engineering and Electromagnetics, BEM/MRM 29
國家United Kingdom
城市The New Forest
期間07-06-0407-06-06

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Mathematics

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  • 引用此

    Chen, C. T., Chen, K. H., Lee, J. F., & Chen, J. T. (2007). Adaptive error estimation of the Trefftz method for solving the Cauchy problem. 於 Boundary Elements and Other Mesh Reduction Methods XXIX (頁 43-56). (WIT Transactions on Modelling and Simulation; 卷 44). https://doi.org/10.2495/BE070051