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Nonlinear Galerkin method with multilevel incremental unknowns. (English) Zbl 0834.65094

Agarwal, R. P. (ed.), Contributions in numerical mathematics. Singapore: World Scientific Publishing Co. World Sci. Ser. Appl. Anal. Vol. 2, 151-164 (1993).
Summary: Multilevel methods are indispensable for the approximation of nonlinear evolution equations when complex physical phenomena involving the interaction of many scales are present (such as in, but without being limited to fluid turbulence). Incremental unknowns of different types have been proposed as means to develop such numerical schemes in the context of finite difference discretizations.
In this article, we present several numerical schemes using the so-called multilevel wavelet-like incremental unknowns. The fully discretized explicit and semiexplicit schemes for reaction-diffusion equations are presented and analyzed. The stability conditions are improved when compared with the corresponding standard algorithms. Furthermore the complexity of the computation on each time step is comparable to the corresponding standard algorithms.
For the entire collection see [Zbl 0829.00032].

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
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