Introduction to finite element methods

Authors:Hans Petter Langtangen Date:Oct 31, 2014

PRELIMINARY VERSION

The finite element method is a powerful tool for solving differential equations. The method can easily deal with complex geometries and higher-order approximations of the solution. Figure Domain for flow around a dolphin shows a two-dimensional domain with a non-trivial geometry. The idea is to divide the domain into triangles (elements) and seek a polynomial approximations to the unknown functions on each triangle. The method glues these piecewise approximations together to find a global solution. Linear and quadratic polynomials over the triangles are particularly popular.

Domain for flow around a dolphin