Shortcomings of existing finite element formulations for subsurface water pollution modeling and its rectification: one-dimensional case

Contaminant transport in an underground system usually occurs in varied flow fields and in anisotropic and heterogenous media. Because the applicability of analytical solutions is extremely limited for such conditions, numerical techniques are essential for underground pollution modeling. Among the numerical techniques, the finite element method has become very popular and is recognized as a powerful numerical tool. The finite element method, particularly for pollution modeling, may be preferable to finite difference because it can link a node with the adjacent nodes in various directions. The main disadvantage with the finite element method is that its mathematical formulations are relatively complicated and follow set rules step by step. In a recent investigation, it was found that such prescribed rules are not applicable everywhere; they have many limitations and shortcomings. Shape functions that transform nodal values into element values are frequently used in an integration process to construct elem...