Convergence analysis of wavelet schemes for convection-reaction equations under minimal regularity assumptions Academic Article

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.

authors

• Popov, Bojan

published proceedings

• SIAM JOURNAL ON NUMERICAL ANALYSIS

author list (cited authors)

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

citation count

• 2

complete list of authors

• Liu, JG||Popov, B||Hong, H||Ewing, RE

publication date

• January 2005

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• Characteristic Method
• Convection-reaction Equation
• Convergence Rate
• Eulerian Lagrangian Method
• Wavelet Method

Digital Object Identifier (DOI)

• 10.1137/S0036142903433832

URI

• https://hdl.handle.net/1969.1/183696

start page

• 521

end page

• 539

volume

• 43

issue

• 2

URL

• http://dx.doi.org/10.1137/s0036142903433832