Adaptive Error Estimation Of The Trefftz
Method For Solving The Cauchy Problem
Author(s)
C.-T. Chen, K.-H. Chen, J.-F. Lee & J.-T. Chen
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.
Keywords: Trefftz method, adaptive error estimation, Cauchy problem, ill-posed
problem, Tikhonov technique, linear regularization method, L-curve concept.
1 Introduction
In 1926, Trefftz [10] presented the Trefftz method for solving boundary value
problems by superimposing the basis functions satisfying the governing
Keywords
Trefftz method, adaptive error estimation, Cauchy problem, ill-posed
problem, Tikhonov technique, linear regularization method, L-curve concept.
Related Book
Other papers in this volume
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