Adaptive finite element heterogeneous multiscale method for homogenization problems

By Assyr Abdulle, Achim Nonnenmacher. 2011

64 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/90b0766d87eab2e81ac0ba7ed297bcf3ea94f8fa

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Yun Bai
2. Assyr Abdulle
3. Björn Engquist
4. Panagiotis E. Souganidis
5. Pingwen Zhang
6. Pingbing Ming

In Computational Theory and Mathematics

1. Yun Bai
2. Assyr Abdulle
3. Björn Engquist
4. Panagiotis E. Souganidis
5. Pingbing Ming
6. Pingwen Zhang

In Mechanics of Materials

1. Yun Bai
2. Assyr Abdulle
3. Björn Engquist
4. Panagiotis E. Souganidis
5. Pingbing Ming
6. Pingwen Zhang

Citations in the corpus

• Adaptive reduced basis finite element heterogeneous multiscale method (2013, methodology): “As the proofs of the theorems are very similar to those in [21], we only sketch them here for completeness.”
• The heterogeneous multiscale method* (2012, unknown): “Under suitable assumptions (Abdulle and Nonnenmacher 2009a, 2011a) (e.g., (H1), (H2) in Section 4.4), one can prove that sup x∈K ‖(a0K − a0(x))∇uH‖L2(K) ≤ C ( HK + ( h ε )2) + eMOD, (4.21) where eMOD is a quantity independent of H,h.”