A Daubechieswavelet Beam Element.

Abstract

In the last years, applying wavelets analysis has called the attention in a wide variety of practical
problems, in particular for the numerical solutions of partial differential equations using different
methods, as finite differences, semi-discrete techniques or finite element method.
Due to function wavelets have the properties of generating a direct sum of L2(R) and that their
correspondent scaling function generates a multiresolution analysis, the wavelet bases in multiple scales
combined with the finite element method provide a suitable strategy for mesh refinement.
In particular, in some mathematical models in mechanics of continuous media, the solutions may
have discontinuities, singularities or high gradients, and it is necessary to approximate with interpolatory
functions having good properties or capacities to efficiently localize those non-regular zones.
In some cases it is useful and convenient to use the Daubechies wavelets, due to their excellent
properties of orthogonality and minimum compact support and for having vanishing moments, providing
guaranty of convergence and accuracy of the approximation in a wide variety of situations.
The present work shows the feasibility of a hybrid scheme using Daubechies wavelet functions and
finite element method to obtain competitive numerical solutions of some classical tests in structural
mechanics.