A Daubechies Wavelet Mindlin-Reissner Plate Element

Abstract

Wavelet multiresolution analysis provides a powerful framework for analyzing functions at various scales. Due to the fact that wavelets have several good properties, such as compact support and vanishing moments, it has gained great interest in solving partial differential equations using the
finite element method. In this paper a two-dimensional wavelet finite element is developed in which the scaling functions are adopted as trial functions. Based on the one-dimensional Daubechies wavelet finite element, that we have constructed recently [Mecánica Computacional Vol XXVI, pp.654-666], tensor product is used to calculate the connection coefficients for stiffness matrices and load vectors. Some test problems are studied and the numerical results are in good agreement with the closed-form or traditional finite elements solutions.