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.


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)