Paper Info
Title
Convergence Analysis of Wavelet Schemes for Convection-Reaction Equations under Minimal Regularity Assumptions
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 $ \mathcal{O}(h/\sqrt{\Delta t} + \Delta 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 $ \mathcal{O}((h/\sqrt{\Delta t})^\theta + (\Delta t)^\theta) $ for initial data in a Besov space $ \displaystyle B^\theta_{2,q} (0
Year
DOI
Venue
2005
10.1137/S0036142903433832
SIAM J. Numerical Analysis
Keywords
Field
DocType
convection-reaction equation,wavelet schemes,minimal regularity assumptions,lower regularity,characteristic method,error estimate,convergence analysis,lagrangian localized adjoint method,generic ellam scheme,displaystyle b,eulerian- lagrangian method,besov space,wavelet method,wavelet scheme,initial data,convection-reaction equations,convergence rate,certain minimal assumption,velocity field,exact solution,finite element method,nuclear waste disposal,finite difference,initial condition,numerical method,first order,numerical simulation
Exact solutions in general relativity,Convergence (routing),Mathematical optimization,Mathematical analysis,Interpolation,Besov space,Operator (computer programming),Rate of convergence,Numerical analysis,Operator theory,Mathematics
Journal
Volume
Issue
ISSN
43
2
0036-1429
Citations 
PageRank 
References 
1
0.39
4
Authors
4
Name
Order
Citations
PageRank
Jiangguo Liu19011.37
Bojan Popov211520.22
Hong Wang311724.13
Richard E. Ewing425245.87