Pre-assembly for FEM 2D non-curvilinear quadrilateral Lagrangian elements

The paper concerns an idea of preparing auxiliary equations and data for the finite element method assembly. This is made for a specific element type and element order and is referred to as the pre-assembly. Most importantly the prepared auxiliary equations require that only the element’s placement (coordinates) needs to be known, while the remaining coefficients that are required are stored in data sheets. The pre-assembly allows programmers who implement the FEM to significantly reduce the effort put into the assembly algorithm through its replacement by a few simple equations and the application of the prepared data. These data sheets can be prepared and can be utilized by FEM programmers. The construction of these data sheets for non-curvilinear quadrilateral Lagrangian elements (of any selected order) is explained in this paper.