Using Interpolation in the Finite Element Method

Abstract

The Method of Finite Elements (MEF) it is an advanced numeric method that allows to obtain an approach of the solution of a contour problem, associated to a differential, ordinary equation or in having derived partial, under certain frontier conditions. This method consists basically, in approaching the solution of a problem of class frontier C2, for the solution of the equivalent problem outlined on a subespacio of finite dimension, that which characterizes and it identifies to the MEF like outline of continuous Galerkin. The base of this space is usually generated by lineal functions that in the case of improving the precision of the solution would have to be carried out a mesh refinement, what leads to the search of algorithms of quick convergence for the resolution of big systems of lineal equations. The fact of elevating the grade of the functions of interpolation polinomial and continuous to pieces, associated to the respective subespacio to each element, it can be another alternative; in this sense, it requires an analysis of the algorithm previously to improve the precision and the time of process computacional. For it, presently work intends the construction of a base of the approach subespacio with the MEF, using a base of functions Spline of natural cubic type. For the evaluation of this method, it has been experienced on a problem of values of contour unidimensional, under the condition boundary of type non homogeneous Dirichlet.