Publication

Error estimates and adaptive finite elements for nonlinear diffusion-convection problems

Jacques Rappaz, Marco Picasso
1996
Journal Articles

Abstract

A priori and a posteriori error estimates are presented for nonlinear diffusion-convection problems when using the classical Streamline Upwind Petrov-Galerkin (SUPG) scheme and numerical integration. For this purpose, an abstract framework is developed. A priori estimates are derived in the H-1 and L(2) norms and the error is bounded above and below by an estimator based on the equation residual. An adaptive algorithm requiring the generation of successive Delaunay triangulations is proposed and numerical results confirm the efficiency of our approach.

Official source

https://infoscience.epfl.ch/entities/publication/9396293e-07ae-4abc-82b6-665d2f107a3b

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Jacques Rappaz, Marco Picasso
1996
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/9396293e-07ae-4abc-82b6-665d2f107a3b

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.

Errors and residuals

In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean).

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

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Error estimates and adaptive finite elements for nonlinear diffusion-convection problems

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