Homogenization of a Continuously Microperiodic Multidimensional Medium

Autores

  • Marcos Pinheiro Lima Universidade Federal do Rio Grande do Sul
  • Leslie Darien Pérez Fernández Universidade Federal de Pelotas
  • Julián Bravo Castillero Universidad de la Habana

DOI:

https://doi.org/10.5540/tema.2018.019.01.15

Resumo

The asymptotic homogenization method is applied to obtain formal asymptotic solution and the homogenized solution of a Dirichlet boundary-value problem for an elliptic equation with rapidly os- cillating coefficients. The proximity of the formal asymptotic solution and the homogenized solution to the exact solution is proved, which provides the mathematical justification of the homogenization pro- cess. Preservation of the symmetry and positive-definiteness of the effective coefficient in the homogenized problem is also proved. An example is presented in order to illustrate the theoretical results.

Biografia do Autor

Marcos Pinheiro Lima, Universidade Federal do Rio Grande do Sul

Institute of Mathematics and Statistics

Leslie Darien Pérez Fernández, Universidade Federal de Pelotas

Department of Mathematics and Statistics

Julián Bravo Castillero, Universidad de la Habana

Facultad de Matemática y Computación

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Publicado

2018-05-05

Como Citar

Lima, M. P., Pérez Fernández, L. D., & Bravo Castillero, J. (2018). Homogenization of a Continuously Microperiodic Multidimensional Medium. Trends in Computational and Applied Mathematics, 19(1), 15. https://doi.org/10.5540/tema.2018.019.01.15

Edição

v. 19 n. 1 (2018)

Seção

Artigo Original

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