FLIM - A Variant of FEM based on Line Integration

A variant of the finite element method (FEM) for modelling and solving partial differential equations based on triangular and tetrahedral meshes is proposed. While FEM is based on integration over finite elements, the new approach - briefly denoted as FLIM hereafter - uses integration along edges (finite lines). The stiffness matrix, which - for linear triangles and tetrahedra - is identical with the one obtained with FEM, as well as the load vector can solely be obtained by summing up the edge contributions. This new variant requires much lower storage than FEM, especially for three-dimensional problems, but yields the same approximation error and convergence rate as the finite element method. It is shown that its performance, when applied to linear problems, is in close agreement with the performance of the finite element method.