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 will allow the student to gather knowledge and fundamental skills to the numerical solution of several kinds of partial differential equations

Numerical methods

Potential theory

Finite differences

Finite elements

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;

- 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;

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;

- 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.