Two-Scale Finite Element Discretizations for Partial Differential Equations (Journal of Computational Mathematics, 2006)
Some two-scale finite element discretizations are introduced for a class of linear partial differential equations. Both boundary value and eigenvalue problems are studied. Based on the two-scale error resolution techniques, several two-scale finite element algorithms are proposed and analyzed. It is shown that this type of two-scale algorithms not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.
Keywords: Finite element; Two-scale discretization; Parallel computation; Sparse grids.