We will present the most common methods to approximate solutions to partial differential equations. Rather than giving an exhaustive list of the most efficient methods used in industrial codes, we will describe the mathematical foundations for the setting and the analysis of the principal methods. Some of them will be implemented with Matlab.
Numerical methods. Scientific computing. Partial differential equations.
Chapter 1. Basics on the theory of linear PDEs, and finite difference methods. Chapter 2. Finite element methods for elliptic problems Chapter 3. Numerical approximation for scalar conservation laws
- To identify the nature of a PDE and the main difficulties for its numerical approximation
- To learn the main categories of numerical methods
- To identify the behavior of the methods and their limitations
- To be able to implement the main methods for simple problems
Evaluation = 60% knowledge + 40% know-how Knowledge = 100% final exam Know-how = 100% continuous assessment