A second order characteristic finite element scheme for convection-diffusion problems. (English) Zbl 1005.65114

Rui, Hongxing; Tabata, Masahisa

Numer. Math. 92, No. 1, 161-177 (2002).

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.

Reviewer: J.Vaníček (Praha)

MSC:

65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
35K15	Initial value problems for second-order parabolic equations
65M25	Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs

Keywords:

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