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