Two-grid finite volume element methods for semilinear parabolic problems
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.
scientific article; zbMATH DE number 5704975
scientific article