The Construction of Plate Finite Elements Usingwavelet Basis Functions

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 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 the shape function to construct elements. Due to their properties, wavelets are very useful when it is necessary to approximate efficiently the solution on non-regular zones. Furthermore, in some cases it is convenient to use the Daubechies wavelet, which has properties of orthogonality and minimum compact support, and provides guaranty of convergence and accuracy of the approximation in a wide variety of situations. The aim of this research is to explore the Galerkin method using wavelets to solve plate bending problems. Some numerical examples, with B-splines and Daubechies, are presented and show the feasibility of our proposal.