Geodesic
The second order projection method in time for the time-dependent natural convection problem
Applications of Mathematics, Tome 61 (2016) no. 3, pp. 299-315 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We consider the second-order projection schemes for the time-dependent natural convection problem. By the projection method, the natural convection problem is decoupled into two linear subproblems, and each subproblem is solved more easily than the original one. The error analysis is accomplished by interpreting the second-order time discretization of a perturbed system which approximates the time-dependent natural convection problem, and the rigorous error analysis of the projection schemes is presented. Our main results of the second order projection schemes for the time-dependent natural convection problem are that the convergence for the velocity and temperature are strongly second order in time while that for the pressure is strongly first order in time.
We consider the second-order projection schemes for the time-dependent natural convection problem. By the projection method, the natural convection problem is decoupled into two linear subproblems, and each subproblem is solved more easily than the original one. The error analysis is accomplished by interpreting the second-order time discretization of a perturbed system which approximates the time-dependent natural convection problem, and the rigorous error analysis of the projection schemes is presented. Our main results of the second order projection schemes for the time-dependent natural convection problem are that the convergence for the velocity and temperature are strongly second order in time while that for the pressure is strongly first order in time.
DOI : 10.1007/s10492-016-0133-y
Classification : 65N15, 65N30, 76D07
Keywords: natural convection problem; projection method; stability; convergence 
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     title = {The second order projection method in time for the time-dependent natural convection problem},
     journal = {Applications of Mathematics},
     pages = {299--315},
     year = {2016},
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Qian, Yanxia; Zhang, Tong. The second order projection method in time for the time-dependent natural convection problem. Applications of Mathematics, Tome 61 (2016) no. 3, pp. 299-315. doi: 10.1007/s10492-016-0133-y

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