caa a22 4500 37888347X CHVBK 20180305123437.0 cr unu---uuuuu 161128e20040901xx s 000 0 eng 10.1515/1569395041931482 doi (NATIONALLICENCE)gruyter-10.1515/1569395041931482 Linß T. Institut für Numerische Mathematik, Technische Universität Dresden, D-01062 Dresden, Germany Layer-adapted meshes for one-dimensional reaction-convection-diffusion problems [Elektronische Daten] [T. Linß] We study convergence properties of an upwinded finite element method for the solution of linear one-dimensional reaction-convection-diffusion problems on arbitrary meshes. We derive conditions that are sufficient for (almost) first-order convergence in the L ∞ norm, uniformly in the diffusion parameter, of the method. These conditions are easy to check and enable one to immediately deduce the rate of convergence. The key ingredients of our analysis are sharp bounds on the W 1,1 norm of the discrete Green's function associated with the discretization. Copyright 2004, Walter de Gruyter Reaction-convection-diffusion nationallicence finite elements nationallicence singular perturbation nationallicence layer-adapted meshes nationallicence Journal of Numerical Mathematics Walter de Gruyter 12/3(2004-09-01), 193-205 1570-2820 12:3<193 2004 12 jnma https://doi.org/10.1515/1569395041931482 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569395041931482 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Linß T. Institut für Numerische Mathematik, Technische Universität Dresden, D-01062 Dresden, Germany NATIONALLICENCE 773 0- Journal of Numerical Mathematics Walter de Gruyter 12/3(2004-09-01), 193-205 1570-2820 12:3<193 2004 12 jnma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter