Generalized difference methods for a nonlinear Dirichlet problem
SIAM Journal on Numerical Analysis
Some errors estimates for the box method
SIAM Journal on Numerical Analysis
Alternating direction multistep methods for parabolic problems-iterative stabilization
SIAM Journal on Numerical Analysis
Some improved error estimates for the modified method of characteristics
SIAM Journal on Numerical Analysis
The finite volume element method for diffusion equations on general triangulations
SIAM Journal on Numerical Analysis
Symmetric modified finite volume element methods for self-adjoint elliptic and parabolic problems
Journal of Computational and Applied Mathematics
A symmetric finite volume scheme for selfadjoint elliptic problems
Journal of Computational and Applied Mathematics
Biquadratic finite volume element methods based on optimal stress points for parabolic problems
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
The finite volume element (FVE) methods used currently are essentially low order and unsymmetric. In this paper, by biquadratic elements and multistep methods, we construct a second order FVE scheme for nonlinear convection diffusion problem on nonuniform rectangular meshes. To overcome the numerical oscillation, we discretize the problem along its characteristic direction. The choice of alternating direction strategy is critical in this paper, which guarantees the high efficiency and symmetry of the discrete scheme. Optimal order error estimates in H^1-norm are derived and a numerical example is given at the end to confirm the usefulness of the method.