96-27
Error Estimates of a Combined Finite Volume - Finite Element Method for Nonlinear Convection - Diffusion Problems
by Feistauer, M.; Felcman, J.; Luk\xe1cov\xe1, M.; Warnecke, G.
Preprint series: 96-27, Preprints
- MSC:
- 65M12 Stability and convergence of numerical methods
- 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
- 35K60 Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE
- 76M10 Finite element methods
- 76M25 Other numerical methods
Abstract: The subject of the paper is the analysis of error estimates of the combined finitevolume - finite element method for the numerical solution of a scalar nonlinearconservation law equation with a diffusion term. Nonlinear convective terms areapproximated with the aid of a monotone finite volume scheme considered over thefinite volume mesh dual to a triangular grid, whereas the diffusion term is discretizedby piecewise linear conforming triangular finite elements. Under the assumptionthat the exact solution possesses some regularity properties and the triangulationsare of weakly acute type, with the aid of the discrete maximum principle and a prioriestimates, error estimates of the method are proved.
Keywords: nonlinear convection-diffusion equation, monotone finite volume schemes,finite element method, numerical integration, discrete maximum principle, a priori estimates, error estimates, compressible Navier--Stokes equations