Numerical Methods for Partial Diferential Equations

Cod: 23031

Department: DCET

Department: DCET

ECTS: 10

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 260

Total contact time: 10

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

- 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;

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;

- Quarteroni, A. Valli, Numerical Approximation of Partial Differential Equations, Springer, 1994;

- Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer, 1995;