论文信息 - Remarks on a posteriori error estimation for finite element solutions

Remarks on a posteriori error estimation for finite element solutions

We utilize the classical hypercircle method and the lowest-order Raviart-Thomas H(div) element to obtain a posteriori error estimates of the P1 finite element solutions for 2D Poisson's equation. A few other estimation methods are also discussed for comparison. We give some theoretical and numerical results to see the effectiveness of the methods.

Fumio Kikuchi | F. Kikuchi | Hironobu Saito | H. Saito

[1] P. Knabner,et al. Numerical Methods for Elliptic and Parabolic Partial Differential Equations , 2003, Texts in Applied Mathematics.

[2] Philippe G. Ciarlet,et al. The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[3] O. C. Zienkiewicz,et al. A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .

[4] Michel Fortin,et al. Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[5] A. Bossavit,et al. A posteriori error bounds by "local corrections" using the dual mesh , 1999 .

[6] L. R. Scott,et al. The Mathematical Theory of Finite Element Methods , 1994 .

[7] Francis Piriou,et al. Error estimators in 3D linear magnetostatics , 2000 .

[8] Philippe Destuynder,et al. Explicit error bounds in a conforming finite element method , 1999, Math. Comput..

[9] Claes Johnson,et al. Computational Differential Equations , 1996 .

[10] J. Oden,et al. A Posteriori Error Estimation in Finite Element Analysis , 2000 .

[11] W. C. Rheinboldt,et al. The hypercircle in mathematical physics , 1958 .