| CODE | MAT5713 | ||||||||||||
| TITLE | Finite Element Analysis | ||||||||||||
| UM LEVEL | 05 - Postgraduate Modular Diploma or Degree Course | ||||||||||||
| MQF LEVEL | 7 | ||||||||||||
| ECTS CREDITS | 15 | ||||||||||||
| DEPARTMENT | Mathematics | ||||||||||||
| DESCRIPTION | Finite element concepts Element shape functions Steady state field problems and some finite element spaces Introduction to FEM for elliptic problems Approximation theory for FEM. Error estimates for elliptic problems FEM for parabolic problems and hyperbolic problems Study-Unit Aims: The aim of this study-unit is to make the student appreciate the theory of this method, and how it could be applied to solve problems in the real world, Finite element methods for differential equations are crucial techniques of the applied computational disciplines. The course focuses classic methods of finding (approximate) finite element solutions. Considered methods are designed for elliptic, parabolic and hyperbolic equations. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Describe and compare the connection between boundary value problems and the finite element method; - Recognise the wide range of applications which can be modelled and solved with the finite element method; - Understand the concepts of weak derivatives, weak solutions and Sobolev spaces; - Understand spacial and temporal discretization for higher dimensional problems; - Understand the applicability and limitations of the methods. 2. Skills: By the end of the study-unit the student will be able to: - Find approximate solution of differential equations by finite element methods. - Obtain a numerical solution to the boundary value problem using suitable shape functions; compare the methods with computer implementations. - Estimate the accuracy of the numerical solution in appropriate norms. Main Text/s and any supplementary readings: - Numerical Solutions of Partial Differential Equations by the Finite Element Method; C. Johnson, Cambridge University Press. - An Introduction to Numerical Analysis, E. Süli and D. Mayers. - Finite Element Methods for Partial Differential Equations, E. SüliSegerlind L.J., Applied Finite Element. Analysis, John Wiley, New York, 2nd Edition, 1984. - Dawe D.J., Matrix and Finite Element Displacement Analysis of Structures, Clarendon Press, Oxford, 1984. - Lewis P.E. and Ward J.P., The Finite Element Method, Principles and Applications, Addison-Wesley, New York, 1991. - Ottosen N.S. and Petersson H., Introduction to the Finite Element Method, Prentice Hall, New York, 1992. - Bathe K.J., Finite Element Procedures, Prentice Hall, New York, 1996. |
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| ADDITIONAL NOTES | Pre-requisite Qualifications: B.Sc. with Mathematics as a main area Follows from: MAT3772 and MAT3712 |
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| STUDY-UNIT TYPE | Lecture and Project | ||||||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Onur Baysal |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years. |
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