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Two-grid finite volume element methods for semilinear parabolic problems. (English) Zbl 1193.65161
The present paper presents a finite volume element method (FVEM) based on two finite element spaces defined on a coarse and a fine grid, applied to a parabolic semilinear problem. An appealing feature is that nonsymmetric and nonlinear problems on a fine space could be regarded as solving a symmetric linear problem on the fine space, plus a nonsymmetric nonlinear problem on the coarse space. The wellposedness of the FVEM is assessed using the Carathéodory theorem, and optimal convergence rates are derived for the one-grid and the two-grid method. Finally, a numerical example illustrates the behavior of the error predicted by the provided theoretical findings.
MSC:
65M08Finite volume methods (IVP of PDE)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
65M55Multigrid methods; domain decomposition (IVP of PDE)
35K55Nonlinear parabolic equations
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