caa a22 4500 465751563 CHVBK 20180323111835.0 cr unu---uuuuu 170327e19900901xx s 000 0 eng 10.1007/BF02250633 doi (NATIONALLICENCE)springer-10.1007/BF02250633 Finite difference schemes on grids with local refinement in time and space for parabolic problems I. Derivation, stability, and error analysis [Elektronische Daten] [R. Ewing, R. Lazarov, P. Vassilevski] Differenz-Schemata für parabolische Probleme auf Gittern mit Lokaler Verdichtung in Zeit und Raum Finite difference schemes for parabolic initial value problems on cell-centered grids in space (rectangular for two space dimensions) with regular local refinement in space as in time are derived and their stability and convergence properties are studied. The construction of the finite difference schemes is based on the finite volume approach by approximation of the balance equation. Thus the derived schemes preserve the mass (or the heat). The approximation at the grid points near the fine and coarse grid interface is based on the approach proposed by the authors in a previous paper for selfadjoint elliptic equations. The proposed schemes are implicit of backward Euler type and are shown to be unconditionally stable. Error analysis is also presented. Springer-Verlag, 1990 Finite difference scheme, cell-centered grids nationallicence local refinement nationallicence refinement in time nationallicence error estimates nationallicence parabolic problem nationallicence Ewing R. Mathematics Department, University of Wyoming, University Station, P.O. Box 3036, 82071, Laramie, Wyoming, USA aut Lazarov R. Institute of Mathematics, Bulgarian Academy of Sciences, "Acad. G. Bontchev”-street, Bl. 8, 1113, Sofia, Bulgaria aut Vassilevski P. Center of Computer Science and Technology, bulgarian Academy of Sciences, "Acad. G. Bontchev”-street, Bl. 25a, 1113, Sofia, Bulgaria aut Computing Springer-Verlag 45/3(1990-09-01), 193-215 0010-485X 45:3<193 1990 45 607 https://doi.org/10.1007/BF02250633 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02250633 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ewing R. Mathematics Department, University of Wyoming, University Station, P.O. Box 3036, 82071, Laramie, Wyoming, USA aut NATIONALLICENCE 700 1- Lazarov R. Institute of Mathematics, Bulgarian Academy of Sciences, "Acad. G. Bontchev”-street, Bl. 8, 1113, Sofia, Bulgaria aut NATIONALLICENCE 700 1- Vassilevski P. Center of Computer Science and Technology, bulgarian Academy of Sciences, "Acad. G. Bontchev”-street, Bl. 25a, 1113, Sofia, Bulgaria aut NATIONALLICENCE 773 0- Computing Springer-Verlag 45/3(1990-09-01), 193-215 0010-485X 45:3<193 1990 45 607 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer