caa a22 4500 463183754 CHVBK 20180406164846.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s10492-007-0013-6 doi (NATIONALLICENCE)springer-10.1007/s10492-007-0013-6 Simplicial finite elements in higher dimensions [Elektronische Daten] [Jan Brandts, Sergey Korotov, Michal Křížek] Over the past fifty years, finite element methods for the approximation of solutions of partial differential equations (PDEs) have become a powerful and reliable tool. Theoretically, these methods are not restricted to PDEs formulated on physical domains up to dimension three. Although at present there does not seem to be a very high practical demand for finite element methods that use higher dimensional simplicial partitions, there are some advantages in studying the methods independent of the dimension. For instance, it provides additional insights into the structure and essence of proofs of results in one, two and three dimensions. In this survey paper we review some recent progress in this direction. Mathematical Institute, Academy of Sciences of Czech Republic, 2007 n -simplex nationallicence finite element method nationallicence superconvergence nationallicence strengthened Cauchy-Schwarz inequality nationallicence discrete maximum principle nationallicence Brandts Jan Korteweg-De Vries Institute for Mathematics, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands aut Korotov Sergey Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK, Finland aut Křížek Michal Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic aut Applications of Mathematics Springer-Verlag 52/3(2007-06-01), 251-265 0862-7940 52:3<251 2007 52 10492 https://doi.org/10.1007/s10492-007-0013-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10492-007-0013-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brandts Jan Korteweg-De Vries Institute for Mathematics, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands aut NATIONALLICENCE 700 1- Korotov Sergey Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK, Finland aut NATIONALLICENCE 700 1- Křížek Michal Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic aut NATIONALLICENCE 773 0- Applications of Mathematics Springer-Verlag 52/3(2007-06-01), 251-265 0862-7940 52:3<251 2007 52 10492 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer