Aproximation Method in Engineering

Code:

MEM100

Acronym:

MAE

Instance: 2005/2006 - 1S

Active?	Yes
Responsible unit:	Mathematics Section
Course/CS Responsible:	Master in Mechanical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
CPGEM	0	Plano de CPGEM 2002	1	1,5	5	-
MEM	9	Plano oficial a partir de 2002	1	1,5	5	-

Teaching language

English

Objectives

The disciple aims to introduce the essential concepts and an unifying basis of the more used numerical methods in computational models in Solid and Fluid Mechanics. It is also expected that the student acquires a broader view of the nature and applicability of these methods and consequently, a more positive attitude to deal with different problems of those previously studied but that may be addressed with the same methods.

Program

General concepts on numerical methods and their importance in engineering. Finite Difference Method in the solution of differential and partial differential equations. Boundary conditions with derivatives. Non-linear problems. Elliptic, parabolic and hyperbolic partial differential equations. Irregular boundaries. Convection /diffusion problems. Upwind schemes. Weighted Residual Method. Approximation with functions that satisfy the boundary conditions. Galerkin Method. Point Collocation Method. Sub-domain Method. Simultaneous approximation of the differential equations and boundary conditions. Weak forms. Convection /diffusion problems: Petrov-Galerkin Method. Variational Methods of Approximation. Critical point of a functional. Euler equations. Essential and natural boundary conditions. Lagrange multipliers and penalty function methods. Ritz Method. Least Squares Method. Partial discretization. Time dependent problems. Numerical time integration of parabolic and hyperbolic partial differential equations. Finite Element Method: brief introduction. Linear and quadratic elements. Natural coordinates. Isoparametric elements. Derivatives and integration. Numerical integration. Finite Volume Method: brief introduction Convection /diffusion problems. Upwind schemes. Boundary element method: brief introduction.

Mandatory literature

O. C. Zienkiewicz and K. Morgan; Finite Element and Applications, ed. Wyley.
Versteeg, H. K.; An introduction to computational fluid dynamics. ISBN: 0-582-21884-5

Complementary Bibliography

Zienkiewicz, O. C.; The finite element method. ISBN: 0-07-084174-8(vol.1)
Math Works; Matlab, The Language of Technical Computing

Teaching methods and learning activities

Theoretical classes consisting on the detailed exposition of the program of the discipline, illustrated with the resolution of engineering application examples. Solution of some problems using MATLAB.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Subject Classes	Participação presencial	24,00
	Total:	-	0,00

Eligibility for exams

Participation in the classes.

Calculation formula of final grade

In the final classification the first evaluation component has a 70% weight and the second component of evaluation has a 30% weight.

Classification improvement

Examination in a date to be designated in the begining of the course.