Paper Info
Title
The decoupled Crank-Nicolson/Adams-Bashforth scheme for the Boussinesq equations with nonsmooth initial data.
Abstract
In this paper, the decoupled Crank–Nicolson/Adams–Bashforth scheme for the Boussinesq equations is considered with nonsmooth initial data. Our numerical scheme is based on the implicit Crank–Nicolson scheme for the linear terms and the explicit Adams–Bashforth scheme for the nonlinear terms for the temporal discretization, standard Galerkin finite element method is used to the spatial discretization. In order to improve the computational efficiency, the decoupled method is introduced, as a consequence the original problem is split into two linear subproblems, and these subproblems can be solved in parallel. We verify that our numerical scheme is almost unconditionally stable for the nonsmooth initial data (u0, θ0) with the divergence-free condition. Furthermore, under some stability conditions, we show that the error estimates for velocity and temperature in L2 norm is of the order O(h2+Δt32), in H1 norm is of the order O(h2+Δt), and the error estimate for pressure in a certain norm is of the order O(h2+Δt). Finally, some numerical examples are provided to verify the established theoretical findings and test the performances of the developed numerical scheme.
Year
DOI
Venue
2018
10.1016/j.amc.2018.04.069
Applied Mathematics and Computation
Keywords
Field
DocType
The Boussinesq equations,Crank–Nicolson/Adams–Bashforth scheme,Decoupled method,Nonsmooth initial data,Stability,Convergence
Discretization,Linear multistep method,Nonlinear system,Temporal discretization,Mathematical analysis,Stability conditions,Norm (mathematics),Mathematics,Crank–Nicolson method,Boussinesq approximation (water waves)
Journal
Volume
ISSN
Citations 
337
0096-3003
0
PageRank 
References 
Authors
0.34
7
3
Name
Order
Citations
PageRank
Tong Zhang15318.56
Jiaojiao Jin200.34
Tao Jiang321144.26