Finite element modelling for nonlinear diffusion equation
Abstract
An FEM algorithm is developed analytically to solve the Burgers equation for one-dimensional nonlinear diffusion. FEs based on both linear and cubic Hermite-polynomial interpolation functions are employed, and numerical results obtained by Crank-Nicholson time marching and iterative solution at each time step are presented in graphs and compared with the exact solutions. The errors of the linear and cubic element formulations are found to be about 0.1 and 0.01 percent, respectively. The possible applicability of the present approach to the Navier-Stokes equations is considered.
- Publication:
-
IN: Finite elements in computational mechanics - FEICOM '85; Proceedings of the International Conference
- Pub Date:
- 1985
- Bibcode:
- 1985fecm....2..853B
- Keywords:
-
- Burger Equation;
- Computational Fluid Dynamics;
- Finite Element Method;
- Nonlinear Equations;
- Diffusion;
- Galerkin Method;
- Interpolation;
- Fluid Mechanics and Heat Transfer