Convergence Analysis of Wavelet Schemes for Convection-Reaction Equations under Minimal Regularity Assumptions
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In this paper, we analyze convergence rates of wavelet schemes for time-dependent convection-reaction equations within the framework of the Eulerian-Lagrangian localized adjoint method (ELLAM). Under certain minimal assumptions that guarantee H 1 -regularity of exact solutions, we show that a generic ELLAM scheme has a convergence rate script O sign(h/ √Δt + Δt) in L 2 -norm. Then, applying the theory of operator interpolation, we obtain error estimates for initial data with even lower regularity. Namely, it is shown that the error of such a scheme is script O sign((h/√Δt) θ + (Δt) θ ) for initial data in a Besov space B 2,qθ (0 < θ < 1, 0 < q ≤ ∞). The error estimates are a priori and optimal in some cases. Numerical experiments using orthogonal wavelets are presented to illustrate the theoretical estimates. © 2005 Society for Industrial and Applied Mathematics.
author list (cited authors)
Liu, J., Popov, B., Wang, H., & Ewing, R. E.