Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation. (English) Zbl 0887.65108

Verfürth, R.

Numer. Math. 78, No. 3, 479-493 (1998).

The author obtains some robust a posteriori error estimators for a singularly perturbed boundary value problem attached to a linear reaction-diffusion equation. The term ‘robust’ is used in the sense that the estimators furnish global upper and local lower bounds in the energy norm, such that the ratio of these bounds is itself bounded from below and above by constants that do neither depend on the meshsize, nor upon the perturbation parameter.

Reviewer: C.I.Gheorghiu (Cluj-Napoca)

MSC:

65N15	Error bounds for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
35B25	Singular perturbations in context of PDEs

Keywords:

singular perturbation; reaction-diffusion equation; a posteriori error estimators; finite element method