Variational Formulation Of Elliptic Partial Differential Equations And Basics In Finite Element Method

Elliptic partial dierential equations appear frequently in various elds of science andrnengineering. These involve equilibrium problems and steady state phenomena. Thernmost common example of such equation is poisson's equation. Most of these physicalrnproblems are very hard to solve analytically, instead, they can be solved numericallyrnusing computational methods. The nite element method is the most popular numericalrnmethod for solving elliptic boundary value problems. In this project, we introducernthe concept of weak formulation, the nite element method, the nite element interpolationrntheory and its application in error estimates of nite element solutions of linearrnelliptic boundary value problems. This project also include the numerical solution of arntwo dimensional poisson equation with dirichlet boundary conditions by nite elementrnmethod.rnKeywords: Weak formulation, Finite Element Method, Poisson Equation

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