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Zbl 0741.65068
Dawson, Clint N.
Godunov-mixed methods for advective flow problems in one space dimension. (English)
[J] SIAM J. Numer. Anal. 28, No.5, 1282-1309 (1991). ISSN 0036-1429; ISSN 1095-7170/e

The author treats numerical solution of the initial-boundary value problem for the nonlinear diffusion equation $s\sb t+f(s)\sb x=(a s\sb x)\sb x$ using a time-splitting method in this interesting paper. A high- order Godunov technique is used for addressing the advective component of the flow and a mixed finite element method is used for the diffusion step. Error estimates are given as well as stability results. Numerical results are described, and an indication of higher dimensional extensions made.
[J.A.Crow (Corvallis)]

MSC 2000:: *65M12 Stability and convergence of numerical methods (IVP of PDE)
65M15 Error bounds (IVP of PDE)
65M60 Finite numerical methods (IVP of PDE)
35K57 Reaction-diffusion equations
35Q35 Other equations arising in fluid mechanics

Keywords: Godunov method; nonlinear diffusion equation; time-splitting method; mixed finite element method; error estimates; stability; numerical results

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