An adaptive variational multiscale method for convection–diffusion problems

The adaptive variational multiscale method is an extension of the variational multiscale method where the line-scale part of the solution is approximated by a sum of numerically computed solutions ...

[1]  M. Larson,et al.  Adaptive variational multiscale methods based on a posteriori error estimation: Energy norm estimates for elliptic problems , 2007 .

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

[3]  Antonio García-Olivares,et al.  Variational subgrid scale formulations for the advection-diffusion-reaction equation , 2001 .

[4]  T. Hughes.  Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .

[5]  Michael J. Holst,et al.  Generalized Green's Functions and the Effective Domain of Influence , 2005, SIAM J. Sci. Comput..

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

[7]  Ruben Juanes,et al.  A variational multiscale finite element method for multiphase flow in porous media , 2005 .

[8]  Graham F. Carey,et al.  A perspective on adaptive modeling and meshing (AM&M) , 2006 .

[9]  Yalchin Efendiev,et al.  Multiscale finite element methods for porous media flows and their applications , 2007 .

[10]  R. Codina.  On stabilized finite element methods for linear systems of convection-diffusion-reaction equations , 2000 .

[11]  T. Hughes,et al.  The variational multiscale method—a paradigm for computational mechanics , 1998 .

[12]  Roy D. Williams,et al.  Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations , 2000 .