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Adaptativité dynamique sur bases d’ondelettes pour l’approximation d’équations aux dérivées partielles. (Dynamical adaptivity using wavelets basis for the approximation of partial differential equations). (French) Zbl 0709.65099

Summary: We present a new concept of adaptivity for the approximation of partial differential equations. The adaptivity is done a priori and not - as in other methods - a posteriori; this is obtained from the use of the decomposition in a wavelet basis that allows to infer the coefficients that are necessary for the representation of the solution. Numerical examples are presented on a one dimensional test problem and the viability of its extension to more dimensions is discussed.

MSC:

65Z05 Applications to the sciences
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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