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We propose an efficient heterogeneous multiscale finite element method based on a local least-squares reconstruction of the effective matrix using the data retrieved from the solution of cell proble...
We propose a condition under which the heterogeneous multiscale 痭ite element method converges for elliptic problem with nonsmooth coe眂ients, and obtain the optimal convergence rate for elliptic prob...
The heterogeneous multiscale method (HMM) is applied to various parabolic problems with multiscale coefficients. These problems can be either linear or nonlinear. Optimal estimates are proved for th...
The surveillance, analysis and ultimately the efficient long-term prediction and control of epidemic dynamics appear to be one of the major challenges nowadays. Detailed atomistic mathematical models ...
We present an overview of the recent development on numerical methods for elliptic problems with multiscale coecients. We carry out a thorough study of two representative techniques: the heterogeneou...

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