Wavelet methods for PDEs — some recent developments
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A fully adaptive wavelet algorithm for parabolic partial differential equations
Applied Numerical Mathematics
An Implementation of Fast Wavelet Galerkin Methods for Integral Equations of the Second Kind
Journal of Scientific Computing
The construction of wavelet finite element and its application
Finite Elements in Analysis and Design
Numerical solution of differential equations using Haar wavelets
Mathematics and Computers in Simulation
A multivariable wavelet-based finite element method and its application to thick plates
Finite Elements in Analysis and Design
A dynamic multiscale lifting computation method using Daubechies wavelet
Journal of Computational and Applied Mathematics
Finite Elements in Analysis and Design
Convergence of an adaptive semi-Lagrangian scheme for the Vlasov-Poisson system
Numerische Mathematik
Multi-scale Daubechies wavelet-based method for 2-D elastic problems
Finite Elements in Analysis and Design
Solving PDEs with the aid of two-dimensional Haar wavelets
Computers & Mathematics with Applications
Review: Wavelet-based numerical analysis: A review and classification
Finite Elements in Analysis and Design
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This paper is concerned with the construction of multiscale wavelet-based elements using lifting scheme. In deriving the computational formulation of multiscale elements of B-spline wavelet on the interval (BSWI), the element displacement field represented by the coefficients of wavelets expansion in wavelet space is transformed into the physical degree of freedoms (DOFs) in finite element space via the corresponding transformation matrix. Then 2D C"0 type multiscale BSWI elements are derived to fulfill the nesting approximation of wavelet finite element method (WFEM). The wavelet-based adaptive algorithm shares the approaches involved in adaptive classical finite element methods. Numerical results indicate that the present multiscale wavelet-based elements are suit for adaptive finite element analysis, especially for singularity problems in engineering. The convergence shown in numerical examples demonstrates the reliability of the elements.