THE CONSTRUCTION OF PLATE FINITE ELEMENTS USING WAVELET BASIS FUNCTIONS

In the last years, applying wavelets analysis has called the attention in a wide variety of practical problems, inparticular for the numerical solutions of partial differential equations using different methods, as finite differences,semi-discrete techniques or the finite element method. In the construction of wavelet-based elements,instead of traditional polynomial interpolation, scaling and wavelet functions have been adopted to form theshape function to construct elements. Due to their properties, wavelets are very useful when it is necessary toapproximate efficiently the solution on non-regular zones. Furthermore, in some cases it is convenient to usethe Daubechies wavelet, which has properties of orthogonality and minimum compact support, and providesguaranty of convergence and accuracy of the approximation in a wide variety of situations. The aim of thisresearch is to explore the Galerkin method using wavelets to solve plate bending problems. Some numericalexamples, with B-splines and Daubechies, are presented and show the feasibility of our proposal.