caa a22 4500 463183746 CHVBK 20180406164846.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s10492-007-0011-8 doi (NATIONALLICENCE)springer-10.1007/s10492-007-0011-8 Space-time discontinuos Galerkin method for solving nonstationary convection-diffusion-reaction problems [Elektronische Daten] [Miloslav Feistauer, Jaroslav Hájek, Karel Švadlenka] The paper presents the theory of the discontinuous Galerkin finite element method for the space-time discretization of a linear nonstationary convection-diffusion-reaction initial-boundary value problem. The discontinuous Galerkin method is applied separately in space and time using, in general, different nonconforming space grids on different time levels and different polynomial degrees p and q in space and time discretization, respectively. In the space discretization the nonsymmetric interior and boundary penalty approximation of diffusion terms is used. The paper is concerned with the proof of error estimates in "L 2(L 2)”-and " $$\sqrt \varepsilon L^2 (H^1 )$$ ”-norms, where ɛ ⩾ 0 is the diffusion coefficient. Using special interpolation theorems for the space as well as time discretization, we find that under some assumptions on the shape regularity of the meshes and a certain regularity of the exact solution, the errors are of order O(h p + τ q ). The estimates hold true even in the hyperbolic case when ɛ = 0. Mathematical Institute, Academy of Sciences of Czech Republic, 2007 nonstationary convection-diffusion-reaction equation nationallicence space-time discontinuous Galerkin finite element discretization nationallicence nonsymmetric treatment of diffusion terms nationallicence error estimates nationallicence Feistauer Miloslav Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 18675, Praha 8, Czech Republic aut Hájek Jaroslav Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 18675, Praha 8, Czech Republic aut Švadlenka Karel Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 18675, Praha 8, Czech Republic aut Applications of Mathematics Springer-Verlag 52/3(2007-06-01), 197-233 0862-7940 52:3<197 2007 52 10492 https://doi.org/10.1007/s10492-007-0011-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10492-007-0011-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Feistauer Miloslav Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 18675, Praha 8, Czech Republic aut NATIONALLICENCE 700 1- Hájek Jaroslav Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 18675, Praha 8, Czech Republic aut NATIONALLICENCE 700 1- Švadlenka Karel Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 18675, Praha 8, Czech Republic aut NATIONALLICENCE 773 0- Applications of Mathematics Springer-Verlag 52/3(2007-06-01), 197-233 0862-7940 52:3<197 2007 52 10492 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer