Outline Homogenization and Numerical Approximation of Elliptic Problems Enrique Zuazua Universidad Aut´onoma de Madrid [email protected] http://www.uam.es/enrique.zuazua Based on joint work with Rafael Orive Santander, December 2006 EnriqueZuazua Homogenization&Numerics Outline Outline 1 Introduction & Motivation 2 The 1−d case 3 The multi-dimensional case 4 The continuous Bloch wave decomposition 5 The Discrete Bloch wave decomposition 6 Numerical experiments 7 Conclusion 8 Open problems 9 Related issues EnriqueZuazua Homogenization&Numerics Outline Outline 1 Introduction & Motivation 2 The 1−d case 3 The multi-dimensional case 4 The continuous Bloch wave decomposition 5 The Discrete Bloch wave decomposition 6 Numerical experiments 7 Conclusion 8 Open problems 9 Related issues EnriqueZuazua Homogenization&Numerics Outline Outline 1 Introduction & Motivation 2 The 1−d case 3 The multi-dimensional case 4 The continuous Bloch wave decomposition 5 The Discrete Bloch wave decomposition 6 Numerical experiments 7 Conclusion 8 Open problems 9 Related issues EnriqueZuazua Homogenization&Numerics Outline Outline 1 Introduction & Motivation 2 The 1−d case 3 The multi-dimensional case 4 The continuous Bloch wave decomposition 5 The Discrete Bloch wave decomposition 6 Numerical experiments 7 Conclusion 8 Open problems 9 Related issues EnriqueZuazua Homogenization&Numerics Outline Outline 1 Introduction & Motivation 2 The 1−d case 3 The multi-dimensional case 4 The continuous Bloch wave decomposition 5 The Discrete Bloch wave decomposition 6 Numerical experiments 7 Conclusion 8 Open problems 9 Related issues EnriqueZuazua Homogenization&Numerics Outline Outline 1 Introduction & Motivation 2 The 1−d case 3 The multi-dimensional case 4 The continuous Bloch wave decomposition 5 The Discrete Bloch wave decomposition 6 Numerical experiments 7 Conclusion 8 Open problems 9 Related issues EnriqueZuazua Homogenization&Numerics Outline Outline 1 Introduction & Motivation 2 The 1−d case 3 The multi-dimensional case 4 The continuous Bloch wave decomposition 5 The Discrete Bloch wave decomposition 6 Numerical experiments 7 Conclusion 8 Open problems 9 Related issues EnriqueZuazua Homogenization&Numerics Outline Outline 1 Introduction & Motivation 2 The 1−d case 3 The multi-dimensional case 4 The continuous Bloch wave decomposition 5 The Discrete Bloch wave decomposition 6 Numerical experiments 7 Conclusion 8 Open problems 9 Related issues EnriqueZuazua Homogenization&Numerics Outline Outline 1 Introduction & Motivation 2 The 1−d case 3 The multi-dimensional case 4 The continuous Bloch wave decomposition 5 The Discrete Bloch wave decomposition 6 Numerical experiments 7 Conclusion 8 Open problems 9 Related issues EnriqueZuazua Homogenization&Numerics