On the accuracy of the finite volume element method for diffusion equations on composite grids
SIAM Journal on Numerical Analysis
The finite volume element method for diffusion equations on general triangulations
SIAM Journal on Numerical Analysis
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Finite volume methods for convection-diffusion problems
SIAM Journal on Numerical Analysis
Point-distributed algorithms on locally refined grids for second order elliptic equations
Scientific computing and applications
A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems
SIAM Journal on Numerical Analysis
| Hi-index | 7.29 |
Recently, new higher order finite volume methods (FVM) were introduced in [Z. Cai, J. Douglas, M. Park, Development and analysis of higher order finite volume methods over rectangles for elliptic equations, Adv. Comput. Math. 19 (2003) 3-33], where the linear system derived by the hybridization with Lagrange multiplier satisfying the flux consistency condition is reduced to a linear system for a pressure variable by an appropriate quadrature rule. We study the convergence of an iterative solver for this linear system. The conjugate gradient (CG) method is a natural choice to solve the system, but it seems slow, possibly due to the non-diagonal dominance of the system. In this paper, we propose block iterative methods with a reordering scheme to solve the linear system derived by the higher order FVM and prove their convergence. With a proper ordering, each block subproblem can be solved by fast methods such as the multigrid (MG) method. The numerical experiments show that these block iterative methods are much faster than CG.