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

11th International Conference on "Mesh methods for boundary-value problems and applications"

Korneev, V.G.^1

Sankt-Petersburg State University, 7/9 Universitetskaya Emb., Saint Petersburg

199034, Russia^1

关键词: Approximate solution;    Basic characteristics;    Computational costs;    Diffusion-reaction equation;    Finite element solution;    Numerical solution;    Quasiuniform meshes;    Reaction diffusion equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012056/pdf
DOI  :  10.1088/1757-899X/158/1/012056

来源: IOP

【 摘 要 】

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. (-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.