Displaying similar documents to “Wavelet approximation methods for pseudodifferential equations: I. Stability and convergence.”

The Mortar Method in the Wavelet Context

Silvia Bertoluzza, Valérie Perrier (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical...

Recent developments in wavelet methods for the solution of PDE's

Silvia Bertoluzza (2005)

Bollettino dell'Unione Matematica Italiana

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After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.

Haar wavelet method for vibration analysis of nanobeams

M. Kirs, M. Mikola, A. Haavajõe, E. Õunapuu, B. Shvartsman, J. Majak (2016)

Waves, Wavelets and Fractals

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In the current study the Haar wavelet method is adopted for free vibration analysis of nanobeams. The size-dependent behavior of the nanobeams, occurring in nanostructures, is described by Eringen nonlocal elasticity model. The accuracy of the solution is explored. The obtained results are compared with ones computed by finite difference method. The numerical convergence rates determined are found to be in agreement with corresponding convergence theorems.

Construction of Non-MSF Non-MRA Wavelets for L²(ℝ) and H²(ℝ) from MSF Wavelets

Aparna Vyas (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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Considering symmetric wavelet sets consisting of four intervals, a class of non-MSF non-MRA wavelets for L²(ℝ) and dilation 2 is obtained. In addition, we obtain a family of non-MSF non-MRA H²-wavelets which includes the one given by Behera [Bull. Polish Acad. Sci. Math. 52 (2004), 169-178].