Mesh Refinement Formulations in Adaptive Finite Element Methods

This paper presents some new ideas for developing adaptive remeshing strategies. It is shown that correct mesh refinement formulations should be defined at an element level rather than a global level. To accomplish this, permissible element errors are required to be defined. This paper describes the methods to determine the permissible element errors. Two mesh refinement formulations are derived according to different accuracy definitions and are compared with the conventional mesh refinement formulation derived at the global level. Numerical examples are shown to explain the features of these mesh refinement formulations. Recommendations are made for use of these mesh refinement formulations.

[1]  I. Babuska,et al.  A‐posteriori error estimates for the finite element method , 1978 .

[2]  O. C. Zienkiewicz,et al.  Error estimates and adaptive refinement for plate bending problems , 1989 .

[3]  Gabriel Bugeda,et al.  A STUDY OF MESH OPTIMALITY CRITERIA IN ADAPTIVE FINITE ELEMENT ANALYSIS , 1993 .

[4]  Ivo Babuška,et al.  Accuracy estimates and adaptive refinements in finite element computations , 1986 .

[5]  E. Hinton,et al.  Edge effects in Mindlin—Reissner plates using adaptive mesh refinement , 1990 .

[6]  Peter Bettess,et al.  Notes on mesh optimal criteria in adaptive finite element computations , 1995 .

[7]  J. W. Bull,et al.  Adaptive analysis of stiffened structures using stiffened plate bending elements , 1996 .

[8]  J. T. Oden,et al.  On the calculation of consistent stress distributions in finite element approximations , 1971 .

[9]  J. N. Reddy,et al.  Note on an approximate method for computing consistent conjugate stresses in elastic finite elements , 1973 .

[10]  John S. Campbell,et al.  Local and global smoothing of discontinuous finite element functions using a least squares method , 1974 .

[11]  O. C. Zienkiewicz,et al.  The superconvergent patch recovery (SPR) and adaptive finite element refinement , 1992 .

[12]  Ivo Babuška,et al.  Validation of A-Posteriori Error Estimators by Numerical Approach , 1994 .

[13]  Gabriel Bugeda,et al.  A general methodology for structural shape optimization problems using automatic adaptive remeshing , 1993 .

[14]  J. W. Bull,et al.  Theoretical formulations for adaptive finite element computations , 1995 .

[15]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique , 1992 .

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

[17]  O. C. Zienkiewicz,et al.  Superconvergent patch recovery techniques – some further tests , 1993 .

[18]  O. C. Zienkiewicz,et al.  A robust triangular plate bending element of the Reissner–Mindlin type , 1988 .

[19]  O. C. Zienkiewicz,et al.  Analysis of thick and thin shell structures by curved finite elements , 1970 .

[20]  P. R. Devloo.  A three-dimensional adaptive finite element strategy , 1991 .