Pedro Serranho

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.