Ten lectures on wavelets
On the representation of operators in bases of compactly supported wavelets
SIAM Journal on Numerical Analysis
An introduction to wavelets
A study of the construction and application of a Daubechies wavelet-based beam element
Finite Elements in Analysis and Design
The construction of wavelet finite element and its application
Finite Elements in Analysis and Design
A multivariable wavelet-based finite element method and its application to thick plates
Finite Elements in Analysis and Design
Finite Elements in Analysis and Design
Journal of Computational and Applied Mathematics
Finite Elements in Analysis and Design
Quadrature rules for numerical integration based on Haar wavelets and hybrid functions
Computers & Mathematics with Applications
A second generation wavelet based finite elements on triangulations
Computational Mechanics
International Journal of Computer Applications in Technology
Finite Elements in Analysis and Design
Journal of Computational and Applied Mathematics
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In the last few years, wavelets analysis application has called the attention of researchers in a wide variety of practical problems, particularly for the numerical solutions of partial differential equations using different methods such as finite differences, semi-discrete techniques or finite element method. In some mathematical models in mechanics of continuous media, the solutions may have local singularities and it is necessary to approximate with interpolatory functions having good properties or capacities to efficiently localize those non-regular zones. Due to their excellent properties of orthogonality and minimum compact support, Daubechies wavelets can be useful and convenient, providing guaranty of convergence and accuracy of the approximation in a wide variety of situations. In this work, we show the feasibility of a hybrid scheme using Daubechies wavelet functions and the finite element method to obtain numerical solutions of some problems in structural mechanics. Following this scheme, the formulations of an Euler-Bernoulli beam element and a Mindlin-Reisner plate element are derived. The accuracy of this approach is investigated in some numerical test cases.