Mixed Arlequin method for multiscale poromechanics problems

Multiscale Hybrid-Mixed Method

This work presents a priori and a posteriori error analyses of a new multiscale hybridmixed method (MHM) for an elliptic model. Specially designed to incorporate multiple scales into the construction of basis functions, this finite element method relaxes the continuity of the primal variable through the action of Lagrange multipliers, while assuring the strong continuity of the normal component...

Mixed Multiscale Methods for Heterogeneous Elliptic Problems

We consider a second order elliptic problem written in mixed form, i.e., as a system of two first order equations. Such problems arise in many contexts, including flow in porous media. The coefficient in the elliptic problem (the permeability of the porous medium) is assumed to be spatially heterogeneous. The emphasis here is on accurate approximation of the solution with respect to the scale o...

Numerical method for elliptic multiscale problems

A mixed multiscale finite element method for elliptic problems with oscillating coefficients

The recently introduced multiscale finite element method for solving elliptic equations with oscillating coefficients is designed to capture the large-scale structure of the solutions without resolving all the fine-scale structures. Motivated by the numerical simulation of flow transport in highly heterogeneous porous media, we propose a mixed multiscale finite element method with an over-sampl...

Homogenization-Based Mixed Multiscale Finite Elements for Problems with Anisotropy

Multiscale finite element numerical methods are used to solve flow problems when the coefficient in the elliptic operator is heterogeneous. A popular mixed multiscale finite element has basis functions which can be defined only over pairs of elements, so we call it a “dual-support” element. We show by example that it can fail to reproduce constant flow fields, and so fails to converge in any me...