A Posteriori Error Estimates for Finite Volume Approximations

A Posteriori Error Estimates for Finite Volume Approximations

We present new a posteriori error estimates for the finite volume approximations of elliptic problems. They are obtained by applying functional a posteriori error estimates to natural extensions of the approximate solution and its flux computed by the finite volume method. The estimates give guaranteed upper bounds for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and...

A Posteriori Error Estimates for Finite Volume Element Approximations of Convection-diffusion-reaction Equations

A Posteriori Error Estimates for Vertex Centered Finite Volume Approximations of Convection-diffusion-reaction Equations

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 de...

A Posteriori Error Estimates for Mixed Finite Element Galerkin Approximations to Second Order Linear Hyperbolic Equations

In this article, a posteriori error analysis for mixed finite element Galerkin approximations of second order linear hyperbolic equations is discussed. Based on mixed elliptic reconstructions and an integration tool, which is a variation of Baker’s technique introduced earlier by G. Baker (SIAM J. Numer. Anal., 13 (1976), 564-576) in the context of a priori estimates for a second order wave equ...

RELIABLE AND EFFICIENT A POSTERIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF THE PARABOLIC p-LAPLACIAN

We generalize the a posteriori techniques for the linear heat equation in [Ver03] to the case of the nonlinear parabolic p-Laplace problem thereby proving reliable and efficient a posteriori error estimates for a fully discrete implicite Euler Galerkin finite element scheme. The error is analyzed using the so-called quasi-norm and a related dual error expression. This leads to equivalence of th...