Consistent robust a posteriori error majorants for approximate solutions of diffusion-reaction equations

Результат исследований: Научные публикации в периодических изданияхстатья в журнале по материалам конференциирецензирование

Аннотация

Efficiency of the error control of numerical solutions of partial differential equations entirely depends on the two factors: accuracy of an a posteriori error majorant and the computational cost of its evaluation for some test function/vector-function plus the cost of the latter. In the paper consistency of an a posteriori bound implies that it is the same in the order with the respective unimprovable a priori bound. Therefore, it is the basic characteristic related to the first factor. The paper is dedicated to the elliptic diffusion-reaction equations. We present a guaranteed robust a posteriori error majorant effective at any nonnegative constant reaction coefficient (r.c.). For a wide range of finite element solutions on a quasiuniform meshes the majorant is consistent. For big values of r.c. the majorant coincides with the majorant of Aubin (1972), which, as it is known, for relatively small r.c. (< ch -2 ) is inconsistent and looses its sense at r.c. approaching zero. Our majorant improves also some other majorants derived for the Poisson and reaction-diffusion equations.

Язык оригиналаанглийский
Номер статьи012056
ЖурналIOP Conference Series: Materials Science and Engineering
Том158
Номер выпуска1
DOI
СостояниеОпубликовано - 19 дек 2016
Событие11th International Conference on Mesh Methods for Boundary-Value Problems and Applications - Kazan, Российская Федерация
Продолжительность: 20 окт 201625 окт 2016

Предметные области Scopus

  • Материаловедение (все)
  • Технология (все)

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