摘要：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.
