Publication

An anisotropic a-posteriori error estimate for a convection-diffusion problem

Luca Formaggia, Paolo Zunino
2001
Journal Articles

Abstract

We develop an a-posteriori error estimation for the finite element simulation of an advection-diffusion problem with anisotropic meshes. The error analysis is carried out by exploiting some recent interpolation error estimates for anisotropic meshes within the a-posteriori analysis framework proposed by Becker and Rannacher (1995, 1996, 1997) and Rannacher (1998). The target application is the transport of a solute (like oxygen or lipids) by the blood stream in a large artery

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https://infoscience.epfl.ch/entities/publication/26f6ede6-12d5-4d20-ba5e-059d99e4ffbe

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Luca Formaggia, Paolo Zunino
2001
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/26f6ede6-12d5-4d20-ba5e-059d99e4ffbe

About this result

Related concepts (30)

Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

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.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

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An anisotropic a-posteriori error estimate for a convection-diffusion problem

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