Some errors estimates for the box method
SIAM Journal on Numerical Analysis
On the accuracy of the finite volume element method for diffusion equations on composite grids
SIAM Journal on Numerical Analysis
On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
SIAM Journal on Numerical Analysis
Mechanical quadrature methods and their extrapolation for solving first kind Abel integral equations
Journal of Computational and Applied Mathematics
Two-grid finite volume element method for linear and nonlinear elliptic problems
Numerische Mathematik
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
An hybrid finite volume-finite element method for variable density incompressible flows
Journal of Computational Physics
An adaptive ghost fluid finite volume method for compressible gas-water simulations
Journal of Computational Physics
International Journal of Computer Mathematics - Splitting Methods for Differential Equations
Journal of Computational Physics
A splitting extrapolation for solving nonlinear elliptic equations with d-quadratic finite elements
Journal of Computational Physics
A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows
Journal of Computational Physics
Hi-index | 7.29 |
This paper is to present a new efficient algorithm by using the finite volume element method and its splitting extrapolation. This method combines the local conservation property of the finite volume element method and the advantages of splitting extrapolation, such as a high order of accuracy, a high degree of parallelism, less computational complexity and more flexibility than a Richardson extrapolation. Because the splitting extrapolation formulas only require us to solve a set of smaller discrete subproblems on different coarser grids in parallel instead of on the globally fine grid, a large scale multidimensional problem is turned into a set of smaller discrete subproblems. Additionally, this method is efficient for solving interface problems if we regard the interfaces of the problems as the interfaces of the initial domain decomposition.