A posteriori estimates for eigenvalue/vector approximations

A posteriori estimates for approximations of time-dependent Stokes equations

In this paper, we derive a posteriori error estimates for space-discrete approximations of the timedependent Stokes equations. By using an appropriate Stokes reconstruction operator, we are able to write an auxiliary error equation, in pointwise form, that satisfies the exact divergence-free condition. Thus, standard energy estimates from partial differential equation theory can be applied dire...

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

Functional a Posteriori Error Estimates for Discontinuous Galerkin Approximations of Elliptic Problems

In this paper, we develop functional a posteriori error estimates for DG approximations of elliptic boundary-value problems. These estimates are based on a certain projection of DG approximations to the respective energy space and functional a posteriori estimates for conforming approximations (see [30, 31]). On these grounds we derive two-sided guaranteed and computable bounds for the errors i...

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...