Error Estimates of a Combined Finite Volume { Finite Element Method for Nonlinear Convection { Diiusion Problems , Mm Aria Lukk a Covv A{medvid'ovv A
نویسندگان
چکیده
The subject of the paper is the analysis of error estimates of the combined nite volume-nite element method for the numerical solution of a scalar nonlinear conservation law equation with a diiusion term. Nonlinear convective terms are approximated with the aid of a monotone nite volume scheme considered over the nite volume mesh dual to a triangular grid, whereas the diiusion term is discretized by piecewise linear conforming triangular nite 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.
منابع مشابه
Global and Localised A Posteriori Error Analysis in the maximum norm for finite element approx- imations of a convection-diffusion problem
We analyse nite element approximations of a stationary convection-diiusion problem. We prove global and localised a posteriori error estimates in the maximum norm. For the discretisation we use the Streamline Diiusion method.
متن کاملA posteriori error estimate for finite volume approximations of nonlinear heat equations
In this contribution we derive a posteriori error estimate for finite volume approximations of nonlinear convection diffusion equations in the L∞(L1)-norm. The problem is discretized implicitly in time by the method of characteristics, and in space by piecewise constant finite volume methods. The analysis is based on a reformulation for finite volume methods. The derived a posteriori error esti...
متن کاملOn Discontinuous Galerkin Methods for Nonlinear Convection-diffusion Problems and Compressible Flow
The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—fi...
متن کاملOn the natural stabilization of convection diffusion problems using LPIM meshless method
By using the finite element $p$-Version in convection-diffusion problems, we can attain to a stabilized and accurate results. Furthermore, the fundamental of the finite element $p$-Version is augmentation degrees of freedom. Based on the fact that the finite element and the meshless methods have similar concept, it is obvious that many ideas in the finite element can be easily used in the meshl...
متن کاملExtension of the Local Problem Error Estimate to the Finite Volume Discretisation
Out of the wide range of a-posteriori error estimates for the Finite Element Method (FEM) of discretisation, the group of estimates based on the element residual seems to be the most popular. One recent extension of the Element Residual Method is the Local Problem Error Estimate (LPEE) 1], which includes the elements of the duality theory and consistently produces good results with the ef-fecti...
متن کامل