In this paper, we develop a computational multiscale method to solve the parabolic wave
approximation with heterogeneous and variable media. Parabolic wave approximation is a …

In this paper, we develop the constrained energy minimizing generalized multiscale finite
element method (CEM-GMsFEM) with mixed boundary conditions (Dirichlet and Neumann) …

In this paper, we propose a local-global multiscale mortar mixed finite element method
(MMMFEM) for multiphase transport in heterogeneous media. It is known that, in the efficient …

In this paper, we develop the constraint energy minimization generalized multiscale finite
element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with …

Geomechanical characteristics should be simulated accurately given their significant effects
on the whole flow patterns in porous media. However, the coupled geomechanics and flow …

In this research, we develop an online enrichment framework for goal-oriented adaptivity
within the generalized multiscale finite element method for flow problems in heterogeneous …

A mixed variational formulation based on a discontinuous Galerkin method for solving the
Darcy problem with a tensor permeability coe cient is considered. Two special hierarchical …

In this thesis, we study the adaptive numerical methods within the framework of generalized
multiscale finite element method (GMsFEM). There are four parts of this work. In this first part …

Goal-oriented adaptivity is introduced within the framework of the Generalized Multiscale
Finite Element Method (GMsFEM) for problems of high-contrast flow. GMsFEM is a flexible …