Convergence Analysis of Wavelet Schemes for Convection-Reaction Equations under Minimal Regularity Assumptions Academic Article uri icon

abstract

  • 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.

published proceedings

  • SIAM Journal on Numerical Analysis

author list (cited authors)

  • Liu, J., Popov, B., Wang, H., & Ewing, R. E.

citation count

  • 2

complete list of authors

  • Liu, Jiangguo||Popov, Bojan||Wang, Hong||Ewing, Richard E

publication date

  • January 2005