Finite Element Method, from the theory to implementation

In the engineering field, there are several approximation techniques allowing to solve the differential equations or the partial derivatives governing the studied phenomena. The most widely used is the Finite Element Method. This method makes it possible to treat any kind of geometry, any kind of boundary value problem arising from electromagnetism, acoustics, fluid mechanics, solid mechanics, biology and even finance! Moreover, This method has a rigorous mathematical approach, based on variational methods. This mathematical approach makes it possible to predict the accuracy of the approximation and to improve it via the error estimates.

The variational problem, an abstract framework Elliptic boundary value problems Finite element method, approximation of boundary value problems Application to selected engineering problems a priori and a posteriori error estimates Finite element method for the evolutionary problems (parabolic and hyperbolic)