Abstract The known a posteriori error analysis of hybrid high-order methods treats the stabilization contribution as part and estimator for an efficient reliable control. This paper circumvents on simplicial meshes arrives at stabilization-free with explicit residual-based adaptive mesh-refining well equilibrium-based guaranteed upper bound (GUB). Numerical evidence in Poisson model problem sup...

A posteriori error estimates for the generalized overlapping domain decomposition method GODDM i.e., with Robin boundary conditions on the interfaces , for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the traces of the subdomain solutions on the interfaces. After discretization of the domain by finite ele...

Abstract. We derive a posteriori error estimates in the L∞((0, T ];L∞(Ω)) norm for approximations of solutions to linear parabolic equations. Using the elliptic reconstruction technique introduced by Makridakis and Nochetto and heat kernel estimates for linear parabolic problems, we first prove a posteriori bounds in the maximum norm for semidiscrete finite element approximations. We then estab...

We study an implicit and discontinuous scheme for a non-local Hamilton-Jacobi equation modelling dislocation dynamics. For the evolution problem, we prove an a posteriori estimate of Crandall-Lions type for the error between continuous and discrete solutions. We deduce an a posteriori error estimate for the effective Hamiltonian associated to a stationary cell problem. In dimension one and unde...

In this note we look at constant-free a posteriori error estimates from a different perspective. We show that they can be interpreted as an alternative way of expressing the residual of a finite element approximation and thus fit into the same framework as other a posteriori error estimates such as residual error indicators. Our approach also reveals that, when applied to singularly perturbed r...

We consider the augmented mixed finite element method introduced in [7] for the equations of plane linear elasticity with mixed boundary conditions. We develop an a posteriori error analysis based on the Ritz projection of the error and obtain an a posteriori error estimator that is reliable and efficient, but that involves a non-local term. Then, introducing an auxiliary function, we derive fu...

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...

A comparative study of aggregation error bounds for the generalized transportation problem is presented. A priori and a posteriori error bounds were derived and a computational study was performed to (a) test the correlation between the a priori, the a posteriori, and the actual error and (b) quantify the difference of the error bounds from the actual error. Based on the results we conclude tha...

This paper presents a voice activity detection (VAD) method using the measurement of a posteriori signal-to-noise ratio (SNR) weighted energy. The motivations are manifold: 1) the difference in frame-to-frame energy provides a great discrimination for speech signals, 2) speech segments, besides their characteristics, are accounted also on their reliability e.g. measured by SNR, 3) the a posteri...