Numerical Analysis and Simulation of PDEs

Recommended Prerequisites

Computational Mathematics.

Teaching Methods

Classes are expository and include examples and exercises for applying the acquired knowledge. As homework the students solve analytical or computational problems that involve the application of the methods studied.

During the semester students may use tutorial time to clarify their difficulties in grasping the theory and in gaining practical knowledge, as well as in the development of the necessary skills for the computational assignment.

Learning Outcomes

The aim of this advanced course is to provide a comprehensive study of theory and applications of modern numerical techniques for the solution of stationary and evolutionary partial differential equations. The course  is built upon a rigorous mathematical basis and addresses fundamental discretization techniques, their error analysis and stability. 

Work Placement(s)

No

Syllabus

Topics may include: linear and non-linear elliptic, parabolic equations, hyperbolic equations, integro-differential   equations; finite difference and finite-volume schemes, spectral collocation and Galerkin-type methods.

Assessment Methods

Assessment
Resolution Problems: 25.0%
Exam: 75.0%

Bibliography

B.S. Jovanovic and E. Süli, Analysis of Finite Difference Schemes For Linear Partial Differential Equations with Generalized Solutions, Springer Series in Computational Mathematics, vol. 46, Springer, London, 2014.

S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 3rd edition, Springer-Verlag, New York, 2008.

R.J. LeVeque, Numerical Methods for Conservation Laws, Birkhäuser, Zurich, 1992.

V. Thommée, Galerkin Finite Element Methods for Parabolic Problems, Springer Series in Computational Mathematics, vol. 25, Springer-Verlag, Berlin Heidelberg, 2006.