Recent Advances in Adaptive Modelling of Heterogeneous Media

[1]  Serge Prudhomme,et al.  On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors , 1999 .

[2]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of polycrystals , 1962 .

[3]  Thomas Y. Hou,et al.  Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients , 1999, Math. Comput..

[4]  J. Oden,et al.  Analysis and adaptive modeling of highly heterogeneous elastic structures , 1997 .

[5]  S. Shtrikman,et al.  On some variational principles in anisotropic and nonhomogeneous elasticity , 1962 .

[6]  Ivo Babuška,et al.  Composites with a Periodic Structure, Mathematical Analysis and Numerical Treatment. , 1985 .

[7]  Kumar Vemaganti,et al.  Hierarchical modeling of heterogeneous solids , 2006 .

[8]  R. Hill The Elastic Behaviour of a Crystalline Aggregate , 1952 .

[9]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[10]  Ivo Babuška,et al.  An approach for constructing families of homogenized equations for periodic media. I: an integral representation and its consequences , 1991 .

[11]  Somnath Ghosh,et al.  Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi Cell finite element method , 1995 .

[12]  E. Sanchez-Palencia Non-Homogeneous Media and Vibration Theory , 1980 .

[13]  R. C. Morgan,et al.  An approach for constructing families of homogenized equations for periodic media. II: properties of the kernel , 1991 .

[14]  Somnath Ghosh,et al.  Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials , 1995 .

[15]  Ivo Babuška,et al.  A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method , 1995 .

[16]  Shaker A. Meguid,et al.  A NOVEL FINITE ELEMENT FOR TREATING INHOMOGENEOUS SOLIDS , 1995 .

[17]  R. V. D. Geijn,et al.  A fast solution method for three‐dimensional many‐particle problems of linear elasticity , 1998 .

[18]  Z. Hashin Analysis of Composite Materials—A Survey , 1983 .

[19]  Thomas Y. Hou,et al.  A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media , 1997 .

[20]  J. Tinsley Oden,et al.  Investigation of the interactions between the numerical and the modeling errors in the Homogenized Dirichlet Projection Method , 1998 .

[21]  Ivo Babuška,et al.  Approximation properties of the h-p version of the finite element method , 1996 .