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
Finite volume methods for convection-diffusion problems
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
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Two low order rectangular finite elements for the convection-diffusion problem with a modified characteristic finite element scheme are studied in this paper. The O(h^2) order error estimates in L^2-norm with respect to the space are obtained for one element with regular meshes and the other under anisotropic meshes. In the process, we use some distinct properties of the interpolation operator, the integral identity technique and the mean value technique, instead of the traditional elliptic projection which is an indispensable tool in the convergence analysis of the previous literature. Finally, some numerical results are provided to verify our theoretical analysis.