Publication

A posteriori error estimates and adaptive finite elements for a nonlinear parabolic problem related to solidification

Marco Picasso, Olivier Krüger
2003
Journal Articles

Abstract

A posteriori error estimates are derived for a nonlinear parabolic problem arising from the isothermal solidification of a binary alloy. Space discretization with continuous, piecewise linear finite elements is considered. The L-2 in time H-1 in space error is bounded above and below by an error estimator based on the equation residual. Numerical results show that the effectivity index is close to one. An adaptive finite element algorithm is proposed and a solutal. dendrite is computed. (C) 2002 Elsevier Science B.V. All rights reserved.

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https://infoscience.epfl.ch/entities/publication/7e16b90a-d7b2-478b-8074-3b57282e62f5

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Marco Picasso, Olivier Krüger
2003
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/7e16b90a-d7b2-478b-8074-3b57282e62f5

About this result

Related concepts (32)

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.

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.

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A posteriori error estimates and adaptive finite elements for a nonlinear parabolic problem related to solidification

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