"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Finite Element and Boundary Element Method
Code
Semes-
ter
Hours: C+S+L
Type
Section
ME281
1
2+2+0
compulsory
Matematica Aplicata
ME281
1
2+2+0
compulsory
Modele matematice în Mecanica si Astronomie
Teaching Staff in Charge
Prof. TRIF Damian, Ph.D.,  dtrifmath.ubbcluj.ro
Aims
The course aims to provide a thorough understanding of mathematical principles, numerical and implementational aspects of the method. Extensive computer exercises shall be regarded as important tools for reaching the major goals.
Content
1. Numerical methods for partial differential equations
2. Finite element method introduction (examples, variational formulation, error estimation, least squares-finite element method)
3. 2D model problems, Poisson equation, computer implementation
4. Abstract formulation
5. Finite element spaces
6. Piecewise linear function - approximation theory
7. Triangulation generation
8. Direct and iterative solvers for large and sparse linear systems
9. Parabolic problems (semi- and complete discretization, discontinuous Galetkin method)
10. Hyperbolic problems (standard Galerkin method, artificial diffusioon, upstream diffusion)
11. Hyperbolic problems - discontinuous Galerkin method
12. Nonlinear problems
13. Boundary element method
14. Finite volume method, particle method
References
1. GHEORGHIU C. I., A constructive introduction in finite element method, Quo Vadis, 1999
2. JIANG B. N., The least-square finite element method, Springer-Verlag, 1998
3. JOHNSON C., Numerical solution of partial differential equations by the finite element method, Cambridge Univ. Press, 1987
4. PETRILA T., GHEORGHIU C. I., Metode element finit si aplicatii, Ed. Academiei, 1986
5. PETRILA T., TRIF D., Metode numerice si computationale in dinamica fluidelor, Ed. Digital Data, Cluj, 2002
6. QUARTERONI A., VALI A., Numerical approximation of partial differential equations, Springer-Verlag, 1994
Assessment
Midterm exam (theory + matlab code) 30%
Final written exam (theory) 60%
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject