On some aspects of the discontinuous Galerkin finite element method for conservation laws
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Journal of Computational and Applied Mathematics
Error estimates for a finite element-finite volume discretization of convection-diffusion equations
Applied Numerical Mathematics
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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The subject of this paper is the analysis of error estimates of the combined finite volume--finite element (FV--FE) 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 a weakly acute type, with the aid of the discrete maximum principle and a priori estimates, error estimates of the method are proved.