On the Reliability of Error Indication Methods for Problems with Uncertain Data

I. Anjam (), O. Mali (), P. Neittaanmäki () and S. Repin ()
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I. Anjam: University of Jyväskylä, Department of Mathematical Information Technology
O. Mali: University of Jyväskylä, Department of Mathematical Information Technology
P. Neittaanmäki: University of Jyväskylä, Department of Mathematical Information Technology
S. Repin: V. A. Steklov Institute of Mathematics in St. Petersburg

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 811-819 from Springer

Abstract: Abstract This paper is concerned with studying the effects of uncertain data in the context of error indicators, which are often used in mesh adaptive numerical methods. We consider the diffusion equation and assume that the coefficients of the diffusion matrix are known not exactly, but within some margins (intervals). Our goal is to study the relationship between the magnitude of uncertainty and reliability of different error indication methods. Our results show that even small values of uncertainty may seriously affect the performance of all error indicators.

Keywords: Error Indicator; Data Uncertainty; Diffusion Matrix; Logical Multiplication Operator; Mean Value Form (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_84

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DOI: 10.1007/978-3-642-33134-3_84

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