caa a22 4500 463183762 CHVBK 20180406164846.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s10492-007-0012-7 doi (NATIONALLICENCE)springer-10.1007/s10492-007-0012-7 Korotov Sergey Institute of Mathematics, Helsinki University of Technology, P. O. Box 1100, FIN-02015 TKK, Finland aut Two-sided a posteriori error estimates for linear elliptic problems with mixed boundary conditions [Elektronische Daten] [Sergey Korotov] The paper is devoted to verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model consisting of a linear elliptic (reaction-diffusion) equation with a mixed Dirichlet/Neumann/Robin boundary condition is considered in this work. On the base of this model, we present simple technologies for straightforward constructing computable upper and lower bounds for the error, which is understood as the difference between the exact solution of the model and its approximation measured in the corresponding energy norm. The estimates obtained are completely independent of the numerical technique used to obtain approximate solutions and are "flexible” in the sense that they can be, in principle, made as close to the true error as the resources of the used computer allow. Mathematical Institute, Academy of Sciences of Czech Republic, 2007 a posteriori error estimation nationallicence error control in energy norm nationallicence two-sided error estimation nationallicence differential equation of elliptic type nationallicence mixed boundary conditions nationallicence Applications of Mathematics Springer-Verlag 52/3(2007-06-01), 235-249 0862-7940 52:3<235 2007 52 10492 https://doi.org/10.1007/s10492-007-0012-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10492-007-0012-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Korotov Sergey Institute of Mathematics, Helsinki University of Technology, P. O. Box 1100, FIN-02015 TKK, Finland aut NATIONALLICENCE 773 0- Applications of Mathematics Springer-Verlag 52/3(2007-06-01), 235-249 0862-7940 52:3<235 2007 52 10492 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer