A Posteriori Error Estimates for Vertex Centered Finite Volume Approximations of Convection-diffusion-reaction Equations
نویسندگان
چکیده
This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation ct+∇·(uf(c))−∇·(D∇c)+λc = 0. The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability of the theoretical results. Mathematics Subject Classification. 65M15, 35K65, 76M25. Received: October 20, 2000. Revised: January 29, 2001.
منابع مشابه
A Posteriori Error Estimates for Finite Volume Element Approximations of Convection-diffusion-reaction Equations
متن کامل
A 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 کاملResidual flux-based a posteriori error estimates for finite volume and related locally conservative methods
We derive in this paper a posteriori error estimates for discretizations of convection–diffusion–reaction equations in two or three space dimensions. Our estimates are valid for any cell-centered finite volume scheme, and, in a larger sense, for any locally conservative method such as the mimetic finite difference, covolume, and other. We consider meshes consisting of simplices or rectangular p...
متن کاملOn Residual-based a Posteriori Error Estimators for Lowest-order Raviart-thomas Element Approximation to Convection-diffusion-reaction Equations
A new technique of residual-type a posteriori error analysis is developed for the lowestorder Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in twoor three-dimension. Both centered mixed scheme and upwind-weighted mixed scheme are considered. The a posteriori error estimators, derived for the stress variable error plus scalar displacement error in...
متن کاملA posteriori $ L^2(L^2)$-error estimates with the new version of streamline diffusion method for the wave equation
In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.
متن کامل