Relative surprise inferences are based on how beliefs change from a priori to a posteriori. As they are based on the posterior distribution of the integrated likelihood, inferences of this type are invariant under relabellings of the parameter of interest. The authors demonstrate that these inferences possess a certain optimality property. Further, they develop computational techniques for impl...

We derive energy-norm a posteriori error bounds for an Euler timestepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For accessibility, we address first the spatially semidiscrete case, and then move to the fully discrete scheme by introducing the implicit Euler timestepping. All results are presented in an abstract setting and then illust...

DATA TYPE See DATA ABSTRACTION ABSTRACTION (The result of) a process of simplification, to describe something at a more general level than the level of detail seen from another point of view. This is often achieved by omitting details specific to individual cases or to methods of implementation. For example, a realtor’s description of a house may leave out architectural detail so that it is an ...

Abstract. This paper establishes a posteriori error analysis for the Stokes equations discretized by an interior penalty type method using H (div) finite elements. The a posteriori error estimator is then employed for designing two grid refinement strategies: one is locally based and the other is globally based. The locally based refinement technique is believed to be able to capture local sing...

In this paper, we establish sharp error estimates of residual type for nite element approximation to elliptic obstacle problems. The estimates are of mixed nature, which are neither of a pure a priori form nor of a pure a posteriori form but instead they are combined by an a priori part and an a posteriori part. The key ingredient in our derivation for the mixed error estimates is the use of a ...

A posteriori error analysis and adaptivity for nite element approximations of hyperbolic problems a Endre S uli The aim of this article is to present an overview of recent developments in the area of a posteriori error estimation for nite element approximations of hyperbolic problems. The approach pursued here rests on the systematic use of hyperbolic duality arguments. We also discuss the ques...

An iterative stochastic algorithm to perform maximum a posteriori parameter estimation of hidden Markov models is proposed. It makes the most of the statistical model by introducing an artiicial probability model based on an increasing number of the unobserved Markov chain at each iteration. Under minor regularity assumptions, we provide suucient conditions to ensure global convergence of this ...

The a posteriori error analysis of conforming finite element discretisations of the biharmonic problem for plates is well established, but nonconforming discretisations are more easy to implement in practice. The a posteriori error analysis for the Morley plate element appears very particular because two edge contributions from an integration by parts vanish simultaneously. This miracle does no...

In this work we introduce and analyse a new adaptive PetrovGalerkin heterogeneous multiscale finite element method (HMM) for monotone elliptic operators with rapid oscillations. In a general heterogeneous setting we prove convergence of the HMM approximations to the solution of a macroscopic limit equation. The major new contribution of this work is an a-posteriori error estimate for the L2-err...