Godunov-mixed methods for advective flow problems in one space dimension. (English) Zbl 0741.65068

Dawson, Clint N.

SIAM J. Numer. Anal. 28, No. 5, 1282-1309 (1991).

The author treats numerical solution of the initial-boundary value problem for the nonlinear diffusion equation \(s_ t+f(s)_ x=(a s_ x)_ x\) 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.

Reviewer: J.A.Crow (Corvallis)

MSC:

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
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K57	Reaction-diffusion equations
35Q35	PDEs in connection with fluid mechanics

Keywords:

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