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1996-27

Error Estimates of a Combined Finite Volume - Finite Element Method for Nonlinear Convection - Diffusion Problems

by Feistauer, M., Felcman, J., Lukácová, M., Warnecke, G..


Series: 1996-27, Preprints

MSC:
65M12 Stability and convergence of numerical methods
65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
35K60 Nonlinear initial value problems for linear parabolic equations
76M10 Finite element methods
76M25 Other numerical methods

Abstract:
subject of the paper is the analysis of error estimates of the combined finite
volume - finite element method for the numerical solution of a scalar nonlinear
conservation law equation with a diffusion term. Nonlinear convective terms are
approximated with the aid of a monotone finite volume scheme considered over the
finite volume mesh dual to a triangular grid, whereas the diffusion term is discretized
by piecewise linear conforming triangular finite elements. Under the assumption
that the exact solution possesses some regularity properties and the triangulations
are of weakly acute type, with the aid of the discrete maximum principle and a priori
estimates, 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