Multiscale Finite Element Methods for Nonlinear Problems and Their Applications

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Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient (2015, unknown): “Consider a set of basis functions”
A new multiscale computational method for elasto-plastic analysis of heterogeneous materials (2012, methodology): “The method has been successfully used for the numerical simulation of the two-phase flow and transport in highly heterogeneous porous media [31‐34] and extended to solve the nonlinear partial differential equations [ 35 ].”
Extended multiscale finite element method for mechanical analysis of heterogeneous materials (2010, methodology): “The MsFEM has been successfully used for the numerical simulation of the twophase flow and transport in highly heterogeneous porous media [34–38] and extended to solving the nonlinear partial differential equations [39].”
Deep Multiscale Model Learning (2018, background): “In general, for nonlinear problems and in the presence of observed solution-related data, multiscale models are challenging to construct [25, 8, 3].”