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/ t + t) 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/t) + (t) ) for initial data in a Besov space B 2,q (0 < < 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.
SIAM Journal on Numerical Analysis
author list (cited authors)
Liu, J., Popov, B., Wang, H., & Ewing, R. E.
complete list of authors
Liu, Jiangguo||Popov, Bojan||Wang, Hong||Ewing, Richard E