论文信息 - Residual-Based A Posteriori Error Estimate for a Nonconforming Reissner-Mindlin Plate Finite Element

Residual-Based A Posteriori Error Estimate for a Nonconforming Reissner-Mindlin Plate Finite Element

Reliable and efficient residual-based a posteriori error estimates are established for the nonconforming finite element method for the Reissner--Mindlin plate due to Arnold and Falk [SIAM J. Numer. Anal., 26 (1989), pp. 1276--1290]. The error is estimated by a computable error estimator from above and below up to multiplicative constants that depend neither on the mesh-size nor on the plate's thickness. The error is controlled in norms that are known to converge to zero in a quasi-optimal way.

Carsten Carstensen | C. Carstensen

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

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

[3] P. Clément. Approximation by finite element functions using local regularization , 1975 .

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

[5] R. Durán,et al. A posteriori error estimators for nonconforming finite element methods , 1996 .

[6] Claes Johnson,et al. Introduction to Adaptive Methods for Differential Equations , 1995, Acta Numerica.

[7] Rüdiger Verfürth,et al. A posteriori error estimation and adaptive mesh-refinement techniques , 1994 .

[8] D. Arnold,et al. A uniformly accurate finite element method for the Reissner-Mindlin plate , 1989 .

[9] C. Carstensen,et al. Constants in Clément-interpolation error and residual based a posteriori estimates in finite element methods , 2000 .

[10] Carsten Carstensen,et al. A posteriori error estimates for nonconforming finite element methods , 2002, Numerische Mathematik.