Variational Formulation of Elliptic Partial Differential Equations and Basics in Finite Element Method
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Date
2016-07-12
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Addis Ababa University
Abstract
Elliptic partial dierential equations appear frequently in various elds of science and
engineering. These involve equilibrium problems and steady state phenomena. The
most common example of such equation is poisson's equation. Most of these physical
problems are very hard to solve analytically, instead, they can be solved numerically
using computational methods. The nite element method is the most popular numerical
method for solving elliptic boundary value problems. In this project, we introduce
the concept of weak formulation, the nite element method, the nite element interpolation
theory and its application in error estimates of nite element solutions of linear
elliptic boundary value problems. This project also include the numerical solution of a
two dimensional poisson equation with dirichlet boundary conditions by nite element
method.
Keywords: Weak formulation, Finite Element Method, Poisson Equation
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Keywords
Weak formulation, Finite Element Method, Poisson Equation