Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
ME281	Finite Element and Boundary Element Method	

Section	Semester	Hours: C+S+L	Category	Type	
Applied Mathematics	1	2+2+0		compulsory	
Mathematical Models in Mechanics and Astronomy - in English	1	2+2+0		compulsory	

Teaching Staff in Charge	Prof. TRIF Damian, Ph.D., dtrif@math.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	
Bibliography	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%