Assessment of discretized errors and adaptive refinement with quadrilateral finite elements

This paper studies discretized errors, and their estimation in conjunction with quadrilateral finite element meshes which are generated by the intelligent mesh generator XFORMQ.1 The exact energy error is used to evaluate the distortion effect of the quadrilateral mesh. The Zienkiewicz–Zhu2 error estimate and actaptive procedure are applied to the short cantilever and the square plate problems using the quadrilateral mesh generator XFORMQ. It is shown that the multistage quadrilateral element refinement produces results superior to the triangular element refinement in the test cases.

[1]  W. Rheinboldt,et al.  Error Estimates for Adaptive Finite Element Computations , 1978 .

[2]  van Lhtm Lambert Beukering,et al.  A general purpose two-dimensional mesh generator , 1978 .

[3]  A. L. Dobyns,et al.  Analysis of Simply-Supported Orthotropic Plates Subject to Static and Dynamic Loads , 1981 .

[4]  Ivo Babuška,et al.  A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis , 1983 .

[5]  D. Owen,et al.  Finite element software for plates and shells , 1984 .

[6]  E. Hinton,et al.  A nine node Lagrangian Mindlin plate element with enhanced shear interpolation , 1984 .

[7]  B. Szabó.  Mesh design for the p-version of the finite element method , 1986 .

[8]  Noboru Kikuchi,et al.  Adaptive grid-design methods for finite delement analysis , 1986 .

[9]  E. Hinton,et al.  A new nine node degenerated shell element with enhanced membrane and shear interpolation , 1986 .

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

[11]  O. C. Zienkiewicz,et al.  Adaptive remeshing for compressible flow computations , 1987 .

[12]  John Robinson,et al.  Distortion measures for quadrilaterals with curved boundaries , 1988 .

[13]  O. C. Zienkiewicz,et al.  Error estimation and adaptivity in flow formulation for forming problems , 1988 .

[14]  O. C. Zienkiewicz,et al.  Error estimates and convergence rates for various incompressible elements , 1989 .

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

[16]  O. Zienkiewicz,et al.  Analysis of the Zienkiewicz–Zhu a‐posteriori error estimator in the finite element method , 1989 .

[17]  H. A. ElMaraghy,et al.  An expert system for forming quadrilateral finite elements , 1990 .