caa a22 4500 605497052 CHVBK 20210128100539.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10543-014-0536-7 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0536-7 An optimal a priori error estimate in the maximum norm for the Il'in scheme in 2D [Elektronische Daten] [H.-G. Roos, M. Schopf] The Il'in scheme is the most famous exponentially fitted finite difference scheme for singularly perturbed boundary value problems. In 1D, Kellogg and Tsan presented a precise error estimate for the scheme from which uniform first order convergence in the discrete maximum norm can be concluded. This estimate is optimal in the sense that one can supply easy examples with smooth data such that the order of uniform convergence of the Il'in scheme is one. In 2D the problem of proving an optimal error estimate remained open. Emel'janov conducted an error analysis giving uniform convergence orders close to one-half. Within the community of singularly perturbed problems it is a legend that this error estimate is sharp. Correcting this mistaken belief it is proven in the present paper that under some conditions the optimal uniform first order convergence of the Il'in scheme in 1D carries over to the two dimensional case. This new result is corroborated by numerical experiments which also shed light on the question in which cases the convergence rate deteriorates. Springer Science+Business Media Dordrecht, 2014 Singular perturbation nationallicence Convection-diffusion nationallicence Il'in scheme nationallicence Difference scheme nationallicence Roos H.-G Technical University of Dresden, Dresden, Germany aut Schopf M. Technical University of Dresden, Dresden, Germany aut BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 1169-1186 0006-3835 55:4<1169 2015 55 10543 https://doi.org/10.1007/s10543-014-0536-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0536-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Roos H.-G Technical University of Dresden, Dresden, Germany aut NATIONALLICENCE 700 1- Schopf M. Technical University of Dresden, Dresden, Germany aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 1169-1186 0006-3835 55:4<1169 2015 55 10543