SOME FINITE ELEMENT SOLUTIONS OF POISSON AND LAPLACE EQUATIONS

Abstract

Poisson and Laplace equations explain various physical phenomena encountered frequently in engineering practice. Some of them are heat conduction, seepage through porous-media, irrotational flow of ideal fluid, distribution of electrical or magnetic potential, torsion of prismatic shaft, bending of prismatic beams and lubrication of pad bearings etc. Being non-linear second order differential equations, it is very difficult(rather impossible) to get a closed form exact solu-tion. Various numerical methods Like Finite Difference Method, Finite Element Method, Relaxation Method and Variational Method have been successfully used'to solve these equations. But Finite Element Method has an edge over these methods owing to sound mathematical background,, ease in representing complex domain and applying boundary conditions. Present work deals with development of computer soft-ware for numerical solution of Laplace and Poisson equations. The Finite Element program developed in. FORTRAN 'IV incorporates numerically integrated isoparametric elements of linear, para-bolic and cubic type. Algdrithm is checke'd for simple cases like Torsion.ground water flow and incompressible fluid flow around a cylinder,. Rigorous studies have teen performed for Stability of structure with cutoffs founded on pervious strata of finite depth. 2. Fluid flow and heat transfer characteristics in non- circular annular passages - involves solution of coupled Poisson equations.