Study of the finite element method

• Grant number: 13/04929-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2013
• End date: May 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: José Alberto Cuminato
• Grantee: Artur Carvalho Santos
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project aims at studying and implementating the finite element methods for boundary value problems for elliptic partial differential equations. We shall study all the prerequisites for the weak formulation of the problem. The Galerkin method is then discussed for a general variational problem. Approximation by piecewise functions will then also be studied and so will mesh generation in two dimensions. Aspects of the convergence of Galerkin method will be discussed in the context of Hilbert spaces suitable for applications. This project work includes no original topic that will lead to publication of results in peer reviewed journals. Given that the student is at the beginning of his undergraduate degree, the work proposed here aims at studying content that will not be seen in depth during the undergraduate course, introducing it to the scientific method and seeking learning simulation techniques that will assist him in his professional life. (AU)