Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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1 module between the following1 module between the following 3 modules among the followingLegend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Numerical methods for partial differential equations (2020/2021)
Teaching code
4S008270
Academic staff
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/08 - NUMERICAL ANALYSIS
Period
II semestre dal Mar 1, 2021 al Jun 11, 2021.
Learning outcomes
The course will discuss the theory and practice of Finite Element and Volume Methods. The theoretical part will follow course notes provided by the Instructor, advanced textbooks on Differential Equations, Iterative Methods for Sparse Linear Systems and numerical methods of Optimization. A part of the course will be held in a Laboratory setting where the methods discussed will be implemented in Matlab, using either the commercial version provided by Mathworks or else the open source version GNU Octave. In addition, high level scientific languages such as FreeFem++ and Clawpack for the numerical solution of elliptic, parabolic and hyperbolic equations will be introduced. At the end of the course the student is expected to have an excellent knowledge of the scientific and computational aspects of the techniques used to solve Partial Differential Equations by means of Finite Elements and Volumes.
Program
The course will discuss the following topics:
* Minimum Principle and the weak form, existence, uniqueness and regularity
* The Rayleigh-Ritz and Galerkin methods, optimization methods, methods for the solution of sparse linear systems
* Transport and Diffusion equations, artificial diffusion, the generalized Galerkin method, discontinuous elements
* Hyperbolic and parabolic equations, semi and completely discretized problems
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| R. J. LeVeque | Finite-Volume Methods for Hyperbolic Problems | Cambridge University Press | 2004 | ||
| Yousef Saad | Iterative Methods for Sparse Linear systems | SIAM | 2013 | ||
| R. J. LeVeque | Numerical Methods for Conservations Laws | Springer | 1992 | ||
| Alfio Quarteroni | Numerical Models for Differential Problems (Edizione 3) | Springer | 2017 |
Examination Methods
The purpose of the exam is to see if the student is able to recall and reproduce the theory and practice of Finite Elements. The exam will be oral. Alternatively, the student may choose to be examined on the basis of a specific software programming language. In this case, part of the evaluation will be replaced by a small project using the package FreeFem++ or Clawpack.
