IMPROVED NUMERICAL SOLUTION ACCURACY OF POISSON'S EQUATION BY ADAPTIVE NODELESS VARIABLE FINITE ELEMENTS WITH FLUX-BASED FORMULATION

A combined nodeless variable finite element method and the flux-based formulation is developed for solving the two-dimensional Poisson's equation. The nodeless variable finite element employs quadratic interpolation functions to provide higher solution accuracy without requiring additional actual nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt automatically with the solution behavior. The accuracy of the combined procedure is evaluated by several problems that have exact solutions.