caa a22 4500 605497079 CHVBK 20210128100539.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10543-014-0534-9 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0534-9 A posteriori error analysis for finite element methods with projection operators as applied to explicit time integration techniques [Elektronische Daten] [J. Collins, D. Estep, S. Tavener] We derive a posteriori error estimates for two classes of explicit finite difference schemes for ordinary differential equations. To facilitate the analysis, we derive a systematic reformulation of the finite difference schemes as finite element methods. The a posteriori error estimates quantify various sources of discretization errors, including effects arising from explicit discretization. This provides a way to judge the relative sizes of the contributions, which in turn can be used to guide the choice of various discretization parameters in order to achieve accuracy in an efficient way. We demonstrate the accuracy of the estimate and the behavior of various error contributions in a set of numerical examples. Springer Science+Business Media Dordrecht, 2014 A posteriori error estimate nationallicence Explicit schemes nationallicence Ordinary differential equations nationallicence Collins J. Department of Mathematics, Chemistry, and Physics, Western Texas A&M University, 79016, Canyon, TX, USA aut Estep D. Department of Statistics, Colorado State University, 80523, Fort Collins, CO, USA aut Tavener S. Department of Mathematics, Colorado State University, 80523, Fort Collins, CO, USA aut BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 1017-1042 0006-3835 55:4<1017 2015 55 10543 https://doi.org/10.1007/s10543-014-0534-9 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/s10543-014-0534-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Collins J. Department of Mathematics, Chemistry, and Physics, Western Texas A&M University, 79016, Canyon, TX, USA aut NATIONALLICENCE 700 1- Estep D. Department of Statistics, Colorado State University, 80523, Fort Collins, CO, USA aut NATIONALLICENCE 700 1- Tavener S. Department of Mathematics, Colorado State University, 80523, Fort Collins, CO, USA aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 1017-1042 0006-3835 55:4<1017 2015 55 10543