Exponential finite element solutions of the diffusion-advection equation
The diffusion-advection equation (DAE) is used in a number of scientific disciplines to model transport of matter or energy in a medium and can help simulate a range of environmental quality problems. A number of numerical methods can be used to solve the equation, including the finite element method (FEM), the boundary element method (BEM) and the finite difference method (FDM). The project develops new numerical techniques, based on exponentially-varying mathematical functions in conjunction with FEM, BEM and FDM, to improve the accuracy and computational efficiency of various DAE solution algorithms. The method is applied to the study of contaminant migration through intact or flawed geo-membrane and clay liner in sanitary landfills.
Abbas El-Zein. 2004. Accuracy Gains from Exponential Discretizations of the Diffusion-Advection Equation. 6th World Congress on Computational Mechanics, Beijing, China, September 2004.
Abbas El-Zein. 2005. Exponential finite elements for diffusion-advection problems. International Journal for Numerical Methods in Engineering, 62(15), 2086-2103.
Abbas El-Zein. 2005. Steady-state diffusion-advection by exponential finite elements. International Journal of Geomechanics ASCE, in press.