Name
Title | ||
|---|---|---|
Covolume-upwind finite volume approximations for linear elliptic partial differential equations |
Abstract | ||
|---|---|---|
In this paper, we study covolume-upwind finite volume methods on rectangular meshes for solving linear elliptic partial differential equations with mixed boundary conditions. To avoid non-physical numerical oscillations for convection-dominated problems, nonstandard control volumes (covolumes) are generated based on local Peclet's numbers and the upwind principle for finite volume approximations. Two types of discretization schemes with mass lumping are developed with use of bilinear or biquadratic basis functions as the trial space respectively. Some stability analyses of the schemes are presented for the model problem with constant coefficients. Various examples are also carried out to numerically demonstrate stability and optimal convergence of the proposed methods. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.jcp.2012.05.004 | J. Comput. Physics |
Keywords | Field | DocType |
nonstandard control volume,convection-dominated problem,stability analysis,constant coefficient,finite volume approximation,covolume-upwind finite volume approximation,covolume-upwind finite volume method,discretization scheme,local peclet,linear elliptic partial differential,biquadratic basis function | Boundary value problem,Discretization,Mathematical optimization,Mathematical analysis,Constant coefficients,Upwind scheme,Basis function,Elliptic partial differential equation,Finite volume method,Finite volume method for one-dimensional steady state diffusion,Mathematics | Journal |
Volume | Issue | ISSN |
231 | 18 | 0021-9991 |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lili Ju | 1 | 444 | 43.43 |
| Li Tian | 2 | 9 | 1.78 |
| Xiao Xiao | 3 | 0 | 0.34 |
| Weidong Zhao | 4 | 35 | 4.74 |