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Effective condition number and superconvergence of the Trefftz method coupled with high order FEM for singularity problems by Hung-Tsai Huang; Zi-Cai Li is a Engineering article available to read on EtoBox.

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The new results of this paper are twofold. (a) For solving the linear algebraic equations AxZb resulting from elliptic equations, we propose the new simplified effective condition number defined by Cond\_EZ jjbjj= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðjjbjj 2 Kb 2 n =Cond: 2 ÞC b 2 n p , where b n Z u T n b, u n is the eigenvector of the minimal eigenvalue of matrix A, and Cond. is the traditional condition number. The Cond\_E may provide a better upper bound of relative errors of x resulting from the perturbation of A and b. (b) To solve the Poisson equation with singularities, the penalty plus hybrid Trefftz method coupled with high order finite element methods (FEM) is used. New superconvergence being the best or almost the best is proven, and verified by numerical experiments for Motz's problem. Compared with the hybrid techniques in Li and Huang [Li ZC, Huang HT. Global superconvergence of simplified hybrid combinations of the Ritz-Galerkin and FEMs of elliptic equations with singularities. II. Lagrange elements and Adini's elements. Appl Numer Math 43;2002:253-73.],

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Author

Hung-Tsai Huang; Zi-Cai Li

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0955-7997)

Published

2006

Language

EN

Field

Engineering (Physical Sciences)