An isogeometric analysis for elliptic homogenization problems

Analysis 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...

Periodic Homogenization of Elliptic Problems (Draft)

Convergence of MsFEM approximations for elliptic, non-periodic homogenization problems

In this work, we are concerned with the convergence of the multiscale finite element method (MsFEM) for elliptic homogenization problems, where we do not assume a certain periodic or stochastic structure, but an averaging assumption which in particular covers periodic and ergodic stochastic coefficients. We also give a result on the convergence in the case of an arbitrary coupling between grid ...

Finite Difference Approximation of Homogenization Problems for Elliptic Equations

In this paper, the problem of the approximation by finite differences of solutions to elliptic problems with rapidly oscillating coefficients and periodic boundary conditions is considered. The mesh-size is denoted by h while ε denotes the period of the rapidly oscillating coefficient. Using Bloch wave decompositions, we analyze the case where the ratio h/ε is rational. We show that if h/ε is k...

Enriched Isogeometric Analysis of Elliptic Boundary Value Problems in Domains with Cracks and/or Corners

The mapping method was introduced in [1] for highly accurate Isogeometric Analysis (IGA) of elliptic boundary value problems containing singularities. The mapping method is concerned with constructions of novel geometrical mappings by which push-forwards of B-splines from the parameter space into the physical space generate singular functions that resemble the singularities. In other words, the...