Two-Scale Finite Element Discretizations for Partial Differential Equations
Keywords:
Finite element, Two-scale discretization, Parallel computation, Sparse grids.Abstract
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.