TY - JOUR

T1 - Consistent robust a posteriori error majorants for approximate solutions of diffusion-reaction equations

AU - Korneev, V. G.

N1 - Publisher Copyright: © Published under licence by IOP Publishing Ltd. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2016/12/19

Y1 - 2016/12/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85014341218&partnerID=8YFLogxK

U2 - 10.1088/1757-899X/158/1/012056

DO - 10.1088/1757-899X/158/1/012056

M3 - Conference article

AN - SCOPUS:85014341218

VL - 158

JO - IOP Conference Series: Materials Science and Engineering

JF - IOP Conference Series: Materials Science and Engineering

SN - 1757-8981

IS - 1

M1 - 012056

T2 - 11th International Conference on Mesh Methods for Boundary-Value Problems and Applications

Y2 - 20 October 2016 through 25 October 2016

ER -