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Zbl 1005.65114
Rui, Hongxing; Tabata, Masahisa
A second order characteristic finite element scheme for convection-diffusion problems. (English)
[J] Numer. Math. 92, No.1, 161-177 (2002). ISSN 0029-599X; ISSN 0945-3245/e

For a convection-diffusion problem a new second-order characteristic finite element scheme is developed. The second-order accuracy of approximation is reached on the time element. The approximations are symmetric and unconditionally stable. On the space $L^2$, the framework for optimal error estimates are suggested. Two numerical examples which show the advantages of the proposed approach are presented.
[J.Vaníček (Praha)]

MSC 2000:: *65M60 Finite numerical methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65M15 Error bounds (IVP of PDE)
35K15 Second order parabolic equations, initial value problems
65M25 Method of characteristics (numerical)

Keywords: convection diffusion problem; second-order characteristic; stability; error bounds; characteristic finite element scheme; numerical examples

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