We prove a posteriori error estimates for a nite element method for systems of strictly hyperbolic conservation laws in one space dimension, and design corresponding adaptive methods. The proof of the a posteriori error estimates is based on a strong stability estimate for an associated dual problem, together with the Galerkin orthogonalityof the nite element method. The strong stability estima...

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...

Abstract. We derive optimal order, residual-based a posteriori error estimates for time discretizations by the two–step BDF method for linear parabolic equations. Appropriate reconstructions of the approximate solution play a key role in the analysis. To utilize the BDF method we employ one step by both the trapezoidal method or the backward Euler scheme. Our a posteriori error estimates are of...

In this paper, we investigate residual-based a posteriori error estimates for the hp finite element approximation of semilinear Neumann boundary elliptic optimal control problems. By using the hp finite element approximation for both the state and the co-state and the hp discontinuous Galerkin finite element approximation for the control, we derive a posteriori error bounds in L2-H1 norms for t...

For the approximation of differential equations residual based error estimates provide upper bounds (usually gross over estimates) to the true error. In this paper we present a procedure for determining values for the constants in the a posteriori estimates which yield accurate estimates to the true error. Numerical experiments demonstrating the effectiveness of the method are given. 2005 Elsev...

We derive a posteriori error estimates for two classes of explicit finite difference schemes for ordinary differential equations. To facilitate the analysis, we derive a systematic reformulation of the finite difference schemes as finite element methods. The a posteriori error estimates quantify various sources of discretization errors, including effects arising from explicit discretization. Th...

We present a new error analysis for finite element approximations of self-adjoint elliptic eigenvalue problems. The analysis consists of three steps. First we prove a posteriori estimates for the error in the approximate eigenvectors and eigenvalues. The error in the eigenvectors is measured both in the L' and energy norms. In these estimates the error is bounded in terms of the mesh size, a st...

In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar firstorder hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each tr...