# Introduction¶

The aim of this document is to report details of the internal of GetFEM useful for developers that have no place in the user documentation. It is also to outline the main prospects for the future development of GetFEM. A list of modifications to be done and main tasks is updated on Savannah https://savannah.nongnu.org/task/?group=getfem.

The GetFEM project focuses on the development of an open source generic finite element library. The goal is to provide a finite element framework which allows to easily build numerical code for the modelisation of system described by partial differential equations (p.d.e.). A special attention is paid to the flexibility of the use of the library in the sense that the switch from a method offered by the library to another is made as easy as possible.

The major point allowing this, compared to traditional finite element codes, is the complete separation between the description of p.d.e. models and finite element methods. Moreover, a separation is made between integration methods (exact or approximated), geometric transformations (linear or not) and finite element methods of arbitrary degrees described on a reference element. GetFEM can be used to build very general finite elements codes, where the finite elements, integration methods, dimension of the meshes, are just some parameters that can be changed very easily, thus allowing a large spectrum of experimentations. Numerous examples are available in the tests directory of the distribution.

The goal is also to make the addition of new finite element method as simple as possible. For standard method, a description of the finite element shape functions and the type of connection of degrees of freedom on the reference element is sufficient. Extensions are provided for Hermite elements, piecewise polynomial, non-polynomial, vectorial elements and XFem. Examples of predefined available methods are $$P_k$$ on simplices in arbitrary degrees and dimensions, $$Q_k$$ on parallelepipeds, $$P_1$$, $$P_2$$ with bubble functions, Hermite elements, elements with hierarchic basis (for multigrid methods for instance), discontinuous $$P_k$$ or $$Q_k$$, XFem, Argyris, HCT, Raviart-Thomas.

The library also includes the usual tools for finite elements such as assembly procedures for classical PDEs, interpolation methods, computation of norms, mesh operations, boundary conditions, post-processing tools such as extraction of slices from a mesh …

The aim of the GetFEM project is not to provide a ready to use finite element code allowing for instance structural mechanics computations with a graphic interface. It is basically a library allowing the build of C++ finite element codes. However, the Python, Scilab and matlab interfaces allows to easily build application coupling the definition of the problem, the finite element methods selection and the graphical post-processing.