Problems of nonlinear computational instability in evolution equations
- Ji Zhongzhen, Lin Wantao, Yang Xiaozhong
- Advances in Atmospheric Sciences
The problem of nonlinear stability of computational schemes is very important in numerical weather forecasts and climate simulations. In this paper, using the heuristic stability analysis method, and concerning a nonlinear advection equation, we compare and contrast the stability criterion of Galerkin Finite Element Method scheme with that of general difference schemes, and especially, point out that the stability criterion of Galerkin FEM scheme approximation is consistent with that of original partial differential equation. Further, the work affirms the superiority of the Galerkin FEM scheme to the general difference schemes on the point-view of computational stability. Finally, several numerical examples on nonlinear stability are given, from which the conditions for nonlinear instability are highlighted.