We study numerical methods for solving a coupled Stokes–Darcy problem in porous media
flow applications. A two-grid method is proposed for decoupling the mixed model by a …

This book covers finite element methods for several typical eigenvalues that arise from
science and engineering. Both theory and implementation are covered in depth at the …

A two-grid discretization scheme is proposed for solving eigenvalue problems, including
both partial differential equations and integral equations. With this new scheme, the solution …

In this paper, an adaptive finite element method for elliptic eigenvalue problems is studied.
Both uniform convergence and optimal complexity of the adaptive finite element eigenvalue …

In this paper, some local and parallel discretizations and adaptive finite element algorithms
are proposed and analyzed for nonlinear elliptic boundary value problems in both two and …

Based on two-grid discretizations, some local and parallel finite element algorithms for the
Stokes problem are proposed and analyzed in this paper. These algorithms are motivated …

Based on two-grid discretizations, in this paper, some new local and parallel finite element
algorithms are proposed and analyzed for the stationary incompressible Navier-Stokes …

Adaptive multilevel finite element methods are developed and analyzed for certain elliptic
systems arising in geometric analysis and general relativity. This class of nonlinear elliptic …

By using new methods for the parallel solution of elliptic partial differential equations, the
teraflops computing power of massively parallel computers can be leveraged to perform …

Domain decomposition methods are a well established tool for an efficient numerical
solution of partial differential equations, in particular for the coupling of different model …