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Two-grid methods for finite volume element approximations of nonlinear parabolic equations. (English) Zbl 1169.65094
The authors prove an error estimate for a finite-volume method for a reaction-diffusion equation on convex polygonal domains in the plane. The reaction term is nonlinear. At each time step the discrete nonlinear equation is solved on a coarse grid, and the result is used as an initial approximation for a Newton iteration on a fine grid.
MSC:
65M55Multigrid methods; domain decomposition (IVP of PDE)
65M15Error bounds (IVP of PDE)
35K57Reaction-diffusion equations
65M06Finite difference methods (IVP of PDE)