Adaptive variational multiscale methods based on a posteriori error estimation: Energy norm estimates for elliptic problems

[1]  I. Babuska,et al.  A feedback element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimator , 1987 .

[2]  V. Thomée,et al.  The stability in _{} and ¹_{} of the ₂-projection onto finite element function spaces , 1987 .

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

[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]  Claes Johnson,et al.  Computational Differential Equations , 1996 .

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

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

[8]  Peter M. Pinsky,et al.  A multiscale finite element method for the Helmholtz equation , 1998 .

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

[10]  Thomas J. R. Hughes,et al.  The Continuous Galerkin Method Is Locally Conservative , 2000 .

[11]  Carsten Carstensen,et al.  Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for H1-stability of the L2-projection onto finite element spaces , 2002, Math. Comput..

[12]  Todd Arbogast,et al.  A two-scale numerical subgrid technique for waterflood simulations , 2002 .

[13]  Ricardo H. Nochetto,et al.  Local problems on stars: A posteriori error estimators, convergence, and performance , 2003, Math. Comput..

[14]  Michael J. Holst,et al.  An Odyssey into Local Refinement and Multilevel Preconditioning III: Implementation and Numerical Experiments , 2003, SIAM J. Sci. Comput..

[15]  M. Larson,et al.  Adaptive Variational Multiscale Methods Based on A Posteriori Error Estimation: Duality Techniques for Elliptic Problems , 2005 .

[16]  Burak Aksoylu,et al.  AN ODYSSEY INTO LOCAL REFINEMENT AND MULTILEVEL PRECONDITIONING II: STABILIZING HIERARCHICAL BASIS METHODS , 2005 .

[17]  Burak Aksoylu,et al.  AN ODYSSEY INTO LOCAL REFINEMENT AND MULTILEVEL PRECONDITIONING I: OPTIMALITY OF THE BPX PRECONDITIONER , 2005 .