PT|EN
Numerical Methods for Partial Diferential Equations
Courses Doctor’s Degree in Applied Mathematics and Modelling
Cod: 23031
Department: DCET
ECTS: 10
Scientific area: Mathematics
Total working hours: 260
Total contact time: 10

This learning unit (LU) will allow the student to gather knowledge and fundamental skills to the numerical solution of several kinds of partial differential equations, including the theoretical analysis of the methods and computational implementation.
Since it is a LU with a strong numerical analysis component, the student should have some background in linear algebra, mathematical and numerical analysis and programming.
Most of the supporting study materials are in english.

 

Numerical methods
Potential theory
Finite differences
Finite elements

- Classify a partial differential equation as elliptic, parabolic or hyperbolic;
- Define a fundamental solution and its importance for the solution of elliptic equations;
- Recognize and numerically approximate the layer potential representations of the solutions;
- Recognize and apply numerical methods to approximate the solutions of several kinds of differential equations;
 

1) Classification of partial differential equations:
a. Elliptic, Parabolic, Hyperbolic.
b. Initial and Boundary conditions: Well-posed problem
2) Potential theory:
a. Fundamental Solution;
b. Layer Potential in the contexto of elliptic equations;
c. Numerical methos for its discretization;
3) Other numerical methods for partial differential equations:
a. Finite difference method;
b. Introduction to the method of finite elements;
 

- Lui: Numerical Analysis of Partial Differential Equations, Wiley, 2012,
- Quarteroni, A. Valli, Numerical Approximation of Partial Differential Equations, Springer, 1994;
- Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer, 1995;

 

Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (60%) and final evaluation (40%). Further information is detailed in the Learning Agreement of the course unit.