Description

Theory/Practice
2

Laboratory
2

Instructors

Luísa Hoffbauer

Contents

(1) DIFFERENTIAL EQUATIONS (1 week)
Introduction
Differential equations and its physicals applications. Boundary value problems and boundary conditions.
Application fields. Examples of boundary value problems:

(2) APPROXIMATION METHODS
FINITE DIFFERENCES METHOD (3 weeks)
WEIGHTED RESIDUAL METHODS (2 weeks)
Least-Squares Approach.
Point Collocation.
Sub-domain Collocation.
Galerkin Method.
VARIATIONAL METHODS (2 weeks)
Basic concepts of variational methods. The variational symbol. Functionals. Total potential energy. Euler equations.
Variational methods of approximation for a solution of a differential equation: Ritz Method.

(3) FINITE ELEMENT METHOD (FEM): AN INTRODUCTION. (3 weeks)
Introduction. A historical note. Application Fields.
FEM analysis of one-dimensional and two-dimensional problems.

(4) SOLUTION OF STRUCTURAL AND THERMICAL PROBLEMS
BY THE FEM METHOD USING MATLAB (2 weeks)

Learning Outcomes

(A) To complete the knowledge acquired in the Numerical Analysis field with emphasis on the application of the Finite Element Method to solve thermal and structural problems in the engineering domain with MATLAB.
(B) Numerical resolution of boundary value problems of 2nd and 4th order using the the Finite Differences Method, variational methods, the Weighted Residual Method and the Finite Elements Method.
(C) To prepare reports based on the carried out analyzes.