6533b827fe1ef96bd1286ea2

RESEARCH PRODUCT

A Unified Approach to Measuring Accuracy of Error Indicators

Pekka NeittaanmäkiOlli MaliImmanuel AnjamSergey Repin

subject

Relation (database)Computer sciencePrincipal (computer security)Functional typeA priori and a posterioriApplied mathematicsBoundary value problemPopularityType I and type II errors

description

In this paper, we present a unified approach to error indication for elliptic boundary value problems. We introduce two different definitions of the accuracy (weak and strong) and show that various indicators result from one principal relation. In particular, this relation generates all the main types of error indicators, which have already gained high popularity in numerical practice. Also, we discuss some new forms of indicators that follow from a posteriori error majorants of the functional type and compare them with other indicators. Finally, we discuss another question related to accuracy of error indicators for problems with incompletely known data.

yearjournalcountryeditionlanguage
2014-01-01
https://doi.org/10.1007/978-94-017-9054-3_1