Aproximation Methods in Engineering

Code:

PRODEM015

Acronym:

MAE

Keywords
Classification	Keyword
OFICIAL	Mechanical Engineering

Instance: 2024/2025 - 2S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
PRODEM	12	Syllabus since 2009/10	1	-	6	28	162

Teaching language

Portuguese

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. 

Learning outcomes and competences

It is 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.

Working method

Presencial

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

Versteeg, H. K.; An introduction to computational fluid dynamics. ISBN: 0-582-21884-5
Zienkiewicz, O. C.; Finite elements and aproximation. ISBN: 0-471-89089-8

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

Designation	Weight (%)
Trabalho escrito	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Elaboração de relatório/dissertação/tese	8,00
Estudo autónomo	130,00
Frequência das aulas	24,00
Total:	162,00

Eligibility for exams

Participation in the classes.

Calculation formula of final grade

In the final classification the evaluation component has a 100% weight.

Classification improvement

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