A DAUBECHIES WAVELET BEAM ELEMENT

VICTORIA VAMPA; MARÍA T. MARTÍN; LILLIAM ALVAREZ DÍAZ

Córdoba, Argentina

Congreso; ENIEF - MACI 2007. Métodos Numéricos y sus Aplicaciones; 2007

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.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.