Partial differential equations (PDEs) describe processes in continua, such as wave propagation, diffusion, and advection. They are used to construct models of the most basic theories underlying physics and engineering. However, in many interesting cases, PDEs are difficult to solve analytically and have to be approximated numerically.
The course gives an introduction to some classes of PDEs and the corresponding finite element type methods for their numerical simulation. Among the target applications are heat conduction, viscous fluid flow and acoustic scattering. Depending on the particular problem, the lecture will discuss the algorithms and the mathematics that underlie the numerical methods as well as their practical implementation.
