Publication

Anisotropic error indicator based on Zienkiewicz-Zhu error estimator: Application to elliptic and parabolic problems

Marco Picasso
2003
Journal Articles

Abstract

The anisotropic error indicator presented in [M. Picasso, Comm. Numer. Methods Engrg., 19 (2003), pp. 13-23.] in the frame of the Laplace equation is extended to elliptic and parabolic problems. Our error indicator is derived using the anisotropic interpolation estimates of [L. Formaggia and S. Perotto, Numer. Math., 89 (2001), pp. 641-667; L. Formaggia and S. Perotto, Numer. Math., (2002), DOI 10.1007/s002110200415], together with a Zienkiewicz-Zhu error estimator to approach the error gradient. A numerical study of the effectivity index is proposed for elliptic, diffusion-convection, and parabolic problems. An adaptive algorithm is implemented, aimed at controlling the relative estimated error.

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https://infoscience.epfl.ch/entities/publication/90d42c16-5d3c-4a5b-a1da-311a53b4f723

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Marco Picasso
2003
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/90d42c16-5d3c-4a5b-a1da-311a53b4f723

About this result

Related concepts (32)

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

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.

Approximation error

The approximation error in a data value is the discrepancy between an exact value and some approximation to it. This error can be expressed as an absolute error (the numerical amount of the discrepancy) or as a relative error (the absolute error divided by the data value). An approximation error can occur for a variety of reasons, among them a computing machine precision or measurement error (e.g. the length of a piece of paper is 4.53 cm but the ruler only allows you to estimate it to the nearest 0.

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Anisotropic error indicator based on Zienkiewicz-Zhu error estimator: Application to elliptic and parabolic problems

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