On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM
- 1 January 2005
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in Multiscale Modeling & Simulation
- Vol. 4 (2) , 447-459
- https://doi.org/10.1137/040607137
Abstract
Heterogeneous multiscale methods have been introduced by E and Engquist (Com- mun. Math. Sci., Vol. 1, No 1, pp. 87-132, 2003) as a methodology for the numerical computation of problems with multiple scales. Analyses of the methods for various homogenization problems have been done by several authors. These results were obtained under the assumption that the micro- scopic models (the cell problems in the homogenization context) are analytically given. For numerical computations, these microscopic models have to be solved numerically. Therefore, it is important to analyze the error transmitted on the macroscale by discretizing the ne scale. We give in this paper H1 and L2 a priori estimates of the fully discrete heterogeneous multiscale nite element method.Keywords
This publication has 8 references indexed in Scilit:
- Heterogeneous Multiscale FEM for Diffusion Problems on Rough SurfacesMultiscale Modeling & Simulation, 2005
- Analysis of the heterogeneous multiscale method for elliptic homogenization problemsJournal of the American Mathematical Society, 2004
- The Heterognous Multiscale MethodsCommunications in Mathematical Sciences, 2003
- Two-scale FEM for homogenization problemsESAIM: Mathematical Modelling and Numerical Analysis, 2002
- Homogenization and MultigridComputing, 2001
- Estimation of Local Modeling Error and Goal-Oriented Adaptive Modeling of Heterogeneous MaterialsJournal of Computational Physics, 2000
- An Introduction to HomogenizationPublished by Oxford University Press (OUP) ,1999
- First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proofProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1997