Finite element-homotopy analysis for nonlinear Poisson equation

摘要

The purpose of this work is to examine the numerical resolution for a classof nonlinear Poisson equations. They are associated to important problems arisingfrom fluid mechanics, steady reaction-diffusion equations, electrostatics, elasticity.The proposed method combines the powerful technique of homotopy analysis and thereliable finite elements. It gives the possibility to consider complex geometry of theproblem's domain both in 2 and in 3 dimensions. The approximate solutions arecompared with the exact solutions in applications and the agreement is very good.Also, the computation proves very good accordance between the two convergenceregions for absolute and relative errors. This is significant for the case the exactsolution is unknown.