Publication

A posteriori analysis of the Chorin-Temam scheme for Stokes equations

Marco Picasso
2013
Journal Articles

Abstract

method) for the time discretization of an unstationary Stokes problem in D c Rd (d = 2,3) given t, f,u0; (P) find (u, p) solution to ult. = u0, ujav = 0 and: au ptAu + V p = f, divu = 0 on (0, T) x D. at Inspired by the analyses of the Backward Euler scheme performed by C. Bernardi and R. Verfiirth, we derive a posteriori estimators for the error on Vu in L2(0, T; L2(D))-norm. Our investigation is supported by numerical experiments. (C)2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

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https://infoscience.epfl.ch/entities/publication/6a4a660a-5d54-44d8-8809-23ebb0bc32aa

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Marco Picasso
2013
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6a4a660a-5d54-44d8-8809-23ebb0bc32aa

About this result

Related concepts (15)

Bayes estimator

In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation. Suppose an unknown parameter is known to have a prior distribution .

Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values.

Maximum a posteriori estimation

In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is closely related to the method of maximum likelihood (ML) estimation, but employs an augmented optimization objective which incorporates a prior distribution (that quantifies the additional information available through prior knowledge of a related event) over the quantity one wants to estimate.

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