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

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationBoundary Elements and Other Mesh Reduction Methods XXIX
Pages43-56
Number of pages14
DOIs
Publication statusPublished - 2007
Event29th 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
Duration: 2007 Jun 42007 Jun 6

Publication series

NameWIT Transactions on Modelling and Simulation
Volume44
ISSN (Print)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
CountryUnited Kingdom
CityThe New Forest
Period07-06-0407-06-06

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Mathematics

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