Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales
نویسندگان
چکیده
منابع مشابه
Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales
A fully discrete analysis of the finite element heterogeneous multiscale method (FEHMM) for elliptic problems with N + 1 well separated scales is discussed. The FEHMM is a numerical homogenization method that relies on macroscopic scheme (macro FEM) for the approximation of the effective solution corresponding to the multiscale problem. The effective data are recovered from micro scale computat...
متن کاملDiscontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales
An analysis of a multiscale symmetric interior penalty discontinuous Galerkin finite element method for the numerical discretization of elliptic problems with multiple scales is proposed. This new method, first described in [A. Abdulle, C.R. Acad. Sci. Paris, Ser. I 346 (2008)] is based on numerical homogenization. It allows to significantly reduce the computational cost of a fine scale discont...
متن کاملAnalysis of the Heterogeneous Multiscale Method for Elliptic Homogenization Problems
A comprehensive analysis is presented for the heterogeneous multiscale method (HMM for short) applied to various elliptic homogenization problems. These problems can be either linear or nonlinear, with deterministic or random coefficients. In most cases considered, optimal estimates are proved for the error between the HMM solutions and the homogenized solutions. Strategies for retrieving the m...
متن کاملDiscontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales
A discontinuous Galerkin finite element heterogeneous multiscale method is proposed for advectiondiffusion problems with highly oscillatory coefficients. The method is based on a coupling of a discontinuous Galerkin discretization for an effective advection-diffusion problem on a macroscopic mesh, whose a priori unknown data are recovered from micro finite element calculations on sampling domai...
متن کاملAn Efficient High Order Heterogeneous Multiscale Method for Elliptic Problems
We propose an efficient heterogeneous multiscale finite element method based on a local least-squares reconstruction of the effective matrix using the data retrieved from the solution of cell problems posed on the vertices of the triangulation. The method achieves high order accuracy for high order macroscopic solver with essentially the same cost as the linear macroscopic solver. Optimal error...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 2014
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/drt066