Multiscale Materials Science: A Mathematical Approach to Defects, Effective Global and Local Behaviors and Uncertainty

Abstract

We focus on developing new mathematical and numerical methods in the context of multiscale materials. We have first addressed questions related to non-periodic modelling, considering heterogeneous materials with defects. Existence and uniqueness of appropriate corrector functions has been shown, along with quantitative results on the quality of the two- scale expansion. Second, we have considered numerical questions related to the MsFEM approach. We have first developed a guaranteed and fully computable a posteriori error estimate, which gives rise to an adaptive discretization procedure. We have also studied how the MsFEM can be adapted to advection-dominated convection-diffusion equations.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 2018
Accession Number
AD1070423

Entities

People

  • Claude Le Bris
  • Frederic Legoll

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Advection
  • Algorithms
  • Boundaries
  • Boundary Layer
  • Computational Complexity
  • Computations
  • Construction
  • Department Of Defense
  • Diffusion
  • Equations
  • Finite Element Analysis
  • Geometry
  • Materials
  • Materials Science
  • Numerical Analysis
  • Two Dimensional
  • Uncertainty

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Theoretical Analysis.