Finite difference approximation of homogenization problems for elliptic equations

Rafael Orive ^[1]
1. [1] Universidad Complutense de Madrid
  
  Universidad Complutense de Madrid
  
  Madrid, España
Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals , Anastasio Pedro Santos Yanguas , 2001, ISBN 8469961446, págs. 447-448
Idioma: inglés
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Resumen
- In this communication, the problem of approximation by finite differences of solutions to elliptic problems with rapidly oscillating coefficients and periodic boundary conditions is considered. We study the case rational dependence between ε, the rapid oscillating period, and h, the size of the numerical grid. Using Bloch wave decompositions, we give explicit error estimates depending on h and the denominator of the ratio h/ε, the scales of numerical homogenization. We may observe that if the ratio h/ε is approximated to an irrational number, recall the convergence to the homogenized problem as in [1].