On first and second order box schemes
Computing
On the accuracy of the finite volume element method for diffusion equations on composite grids
SIAM Journal on Numerical Analysis
On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems
SIAM Journal on Numerical Analysis
On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
SIAM Journal on Numerical Analysis
Error Estimates for a Finite Volume Element Method for Elliptic PDEs in Nonconvex Polygonal Domains
SIAM Journal on Numerical Analysis
Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)
Hi-index | 0.00 |
In this paper, we study finite volume element (FVE) method for convection-diffusion-reaction equations in a two-dimensional convex polygonal domain. These types of equations arise in the modeling of a waste scenario of a radioactive contaminant transport and reaction in flowing groundwater. Both spatially discrete scheme and discrete-in-time scheme are analyzed in this paper. For the spatially discrete scheme, optimal order error estimates in L2 and H1 norms are obtained for the homogeneous equation using energy method. Further, a quasi-optimal order error estimate in L∞ norm is shown to hold in an interior subdomain away from the corners. Based on backward Euler method, a time discretization scheme is discussed and related error estimates are derived.