Computational Partial Differential Equations with Finite Elements
The mathematical models arising from countless physical and natural phenomena as well as social sciences such as economics and finance are based on Partial Differential Equations (PDEs). The solution of PDE problems of practical importance is rarely available in closed form, hence the need for computational methods able to deliver accurate and reliable numerical (approximate) solutions.
This module provides the mathematical foundation as well as practical implementation knowledge of computational schemes for PDEs, using Finite Differences (FD) and Finite Element Methods (FEM). You will learn fundamental properties of numerical methods (consistency, stability, convergence) and how to use these notions to select the right method depending on the type of PDE problem that needs to be solved. A peculiarity of the FEM is that it has a very strong theoretical grounding in the field of functional analysis, so you will also acquire a sound knowledge of functional spaces and their application to the numerical analysis of FEM.