The
paper presents an idea based on [2] elements with „legs”. Newly proposed
element is built on a kind of Lagrange interpolation and gives us the
possibility to generate the stiffness matrix for highly irregular meshes
without lose of continuity of the function on the elements’ edges. Degrees of
freedom are treated as the approximated value of solution function. Moreover,
such kind of elements and their shape functions fulfill all conditions stated
by Finite Elements For this kind of approximation some elements in the mesh are
not defined a-priori as obvious. This requires creation of these
elements (their shape functions) individually just before, or at same time as
its stiffness matrixes. The quantity of nodes and the shape functions for such
elements are finally defined by ultimate mesh configuration so this allows to
freely construct the mesh configuration (refining) during adaptive process.
This algorithm can be used for arbitrary chosen interpolation of Lagrange type
i.e. for arbitrary set of interpolation nodes and its placement. In special
case one can obtain the classical elements (CST, LST , Q2 etc.)