Paper Info
Title
A two-grid combined finite element-upwind finite volume method for a nonlinear convection-dominated diffusion reaction equation
Abstract
In this paper, we first present a combined finite element-upwind finite volume method for a fully nonlinear convection-dominated diffusion reaction equation and derive its a priori optimal error estimate in H1-norm and sub-optimal error estimate in L2-norm for piecewise linear finite element combining with the first order upwind finite volume scheme. Then we study a type of two-grid method for the nonlinear convection-dominated transport equation together with the combined finite element-upwind finite volume method on the fine grid Th and the streamline diffusion finite element scheme on the coarse grid TH, which not only significantly reduces the computational cost on nonlinear iterations but also remains the numerical computation stabilized and the approximation accuracy unchanged. A priori error estimate of such designed two-grid method in H1-norm is proved to be O(h+H32), showing that the two-grid method achieves the optimal approximation as long as the mesh sizes satisfy h=O(H32). Finally, a numerical example is carried out to verify the accuracy and efficiency of the present numerical method.
Year
DOI
Venue
2015
10.1016/j.cam.2015.03.059
Journal of Computational and Applied Mathematics
Keywords
Field
DocType
Two-grid method,A combined finite element-upwind finite volume method,Nonlinear,Convection-dominated,Error estimate
Mathematical optimization,Mathematical analysis,Extended finite element method,Finite element method,Finite difference coefficient,Streamline diffusion,Numerical analysis,Finite volume method,Mathematics,Finite volume method for one-dimensional steady state diffusion,Mixed finite element method
Journal
Volume
Issue
ISSN
288
C
0377-0427
Citations 
PageRank 
References 
0
0.34
4
Authors
4
Name
Order
Citations
PageRank
Mingyan He141.90
Pengtao Sun22810.06
Cheng Wang35811.05
Ziping Huang453.35